Singularities of the Prym theta divisor

Abstract

For the Jacobian of a curve, the Riemann singularity theorem gives a geometric interpretation of the singularities of the theta divisor in terms of special linear series on the curve. This paper proves an analogous theorem for Prym varieties. Applications of this theorem to cubic threefolds and Prym varieties of dimension five are also considered.

  • [acgh] E. Arbarello, M. Cornalba, P. A. Griffiths, and J. Harris, Geometry of Algebraic Curves. I, New York: Springer-Verlag, 1985.
    @book{acgh, MRKEY = {770932},
      AUTHOR = {Arbarello, E. and Cornalba, M. and Griffiths, P. A. and Harris, J.},
      TITLE = {Geometry of {A}lgebraic {C}urves. {{\rm I}}},
      SERIES = {Grundl. Math. Wissen.},
      NUMBER = {267},
      PUBLISHER = {Springer-Verlag},
      ADDRESS = {New York},
      YEAR = {1985},
      PAGES = {xvi+386},
      ISBN = {0-387-90997-4},
      MRCLASS = {14Hxx (14-02)},
      MRNUMBER = {86h:14019},
      ZBLNUMBER = {0559.14017},
      MRREVIEWER = {Werner Kleinert},
      }
  • [b1] Go to document A. Beauville, "Prym varieties and the Schottky problem," Invent. Math., vol. 41, iss. 2, pp. 149-196, 1977.
    @article{b1, MRKEY = {0572974},
      AUTHOR = {Beauville, Arnaud},
      TITLE = {Prym varieties and the {S}chottky problem},
      JOURNAL = {Invent. Math.},
      FJOURNAL = {Inventiones Mathematicae},
      VOLUME = {41},
      YEAR = {1977},
      NUMBER = {2},
      PAGES = {149--196},
      ISSN = {0020-9910},
      MRCLASS = {14H15 (30A46)},
      MRNUMBER = {58 \#27995},
      DOI = {10.1007/BF01418373},
      ZBLNUMBER = {0333.14013},
      MRREVIEWER = {M. Fried},
      }
  • [b2] Go to document A. Beauville, "Variétés de Prym et jacobiennes intermédiaires," Ann. Sci. École Norm. Sup., vol. 10, iss. 3, pp. 309-391, 1977.
    @article{b2, MRKEY = {0472843},
      AUTHOR = {Beauville, Arnaud},
      TITLE = {Variétés de {P}rym et jacobiennes intermédiaires},
      JOURNAL = {Ann. Sci. École Norm. Sup.},
      FJOURNAL = {Annales Scientifiques de l'École Normale Supérieure. Quatrième Série},
      VOLUME = {10},
      YEAR = {1977},
      NUMBER = {3},
      PAGES = {309--391},
      ISSN = {0012-9593},
      MRCLASS = {14K30 (14C30 14J99 14M20)},
      MRNUMBER = {57 \#12532},
      URL = {http://www.numdam.org/item?id=ASENS_1977_4_10_3_309_0},
      ZBLNUMBER = {0368.14018},
      MRREVIEWER = {T. Oda},
      }
  • [b0] A. Beauville, "Les singularités du diviseur $\Theta $ de la jacobienne intermédiaire de l’hypersurface cubique dans ${\bf P}^{4}$," in Algebraic Threefolds, Conte, A., Ed., New York: Springer-Verlag, 1982, pp. 190-208.
    @incollection{b0, MRKEY = {672617},
      AUTHOR = {Beauville, Arnaud},
      EDITOR = {Conte, Alberto},
      TITLE = {Les singularités du diviseur {$\Theta $} de la jacobienne intermédiaire de l'hypersurface cubique dans {${\bf P}\sp{4}$}},
      BOOKTITLE = {Algebraic Threefolds},
      VENUE = {Varenna, 1981},
      SERIES = {Lecture Notes in Math.},
      NUMBER = {947},
      PAGES = {190--208},
      PUBLISHER = {Springer-Verlag},
      ADDRESS = {New York},
      YEAR = {1982},
      MRCLASS = {14J30 (14C30 14J10 14K30)},
      MRNUMBER = {84c:14030},
      ZBLNUMBER = {0492.14033},
      MRREVIEWER = {C. A. M. Peters},
      }
  • [b3] Go to document A. Beauville, "Determinantal hypersurfaces," Michigan Math. J., vol. 48, pp. 39-64, 2000.
    @article{b3, MRKEY = {1786479},
      AUTHOR = {Beauville, Arnaud},
      TITLE = {Determinantal hypersurfaces},
      INVNOTE = {Dedicated to William Fulton on the occasion of his 60th birthday},
      JOURNAL = {Michigan Math. J.},
      FJOURNAL = {The Michigan Mathematical Journal},
      VOLUME = {48},
      YEAR = {2000},
      PAGES = {39--64},
      ISSN = {0026-2285},
      MRCLASS = {14M12 (14J70)},
      MRNUMBER = {2002b:14060},
      ZBLNUMBER = {1076.14534},
      DOI = {10.1307/mmj/1030132707},
      MRREVIEWER = {Laurent Manivel},
      }
  • [birlange] H. Lange and C. Birkenhake, Complex Abelian Varieties, New York: Springer-Verlag, 1992.
    @book{birlange, MRKEY = {1217487},
      AUTHOR = {Lange, Herbert and Birkenhake, Christina},
      TITLE = {Complex {A}belian {V}arieties},
      SERIES = {Grundl. Math. Wissen.},
      NUMBER = {302},
      PUBLISHER = {Springer-Verlag},
      ADDRESS = {New York},
      YEAR = {1992},
      PAGES = {viii+435},
      ISBN = {3-540-54747-9},
      MRCLASS = {14-02 (14Kxx 32G20)},
      MRNUMBER = {94j:14001},
      ZBLNUMBER = {0779.14012},
      MRREVIEWER = {Olivier Debarre},
      }
  • [cmf] S. Casalaina-Martin and R. Friedman, "Cubic threefolds and abelian varieties of dimension five," J. Algebraic Geom., vol. 14, iss. 2, pp. 295-326, 2005.
    @article{cmf, MRKEY = {2123232},
      AUTHOR = {Casalaina-Martin, Sebastian and Friedman, Robert},
      TITLE = {Cubic threefolds and abelian varieties of dimension five},
      JOURNAL = {J. Algebraic Geom.},
      FJOURNAL = {Journal of Algebraic Geometry},
      VOLUME = {14},
      YEAR = {2005},
      NUMBER = {2},
      PAGES = {295--326},
      ISSN = {1056-3911},
      MRCLASS = {14K12 (14J30 14K30)},
      MRNUMBER = {2006g:14071},
      ZBLNUMBER = {1082.14047},
      MRREVIEWER = {M. Kh. Gizatullin},
      }
  • [cg] Go to document H. C. Clemens and P. A. Griffiths, "The intermediate Jacobian of the cubic threefold," Ann. of Math., vol. 95, pp. 281-356, 1972.
    @article{cg, MRKEY = {0302652},
      AUTHOR = {Clemens, C. Herbert and Griffiths, Phillip A.},
      TITLE = {The intermediate {J}acobian of the cubic threefold},
      JOURNAL = {Ann. of Math. },
      FJOURNAL = {Annals of Mathematics. Second Series},
      VOLUME = {95},
      YEAR = {1972},
      PAGES = {281--356},
      ISSN = {0003-486X},
      MRCLASS = {14J10 (14G13 14J05 14K20 14M20 14N99)},
      MRNUMBER = {46 \#1796},
      DOI = {10.2307/1970801},
      ZBLNUMBER = {0245.14010},
      MRREVIEWER = {H. Popp},
      }
  • [debarre] Go to document O. Debarre, "Sur le probleme de Torelli pour les varieties de Prym," Amer. J. Math., vol. 111, iss. 1, pp. 111-134, 1989.
    @article{debarre, MRKEY = {980302},
      AUTHOR = {Debarre, Olivier},
      TITLE = {Sur le probleme de {T}orelli pour les varieties de {P}rym},
      JOURNAL = {Amer. J. Math.},
      FJOURNAL = {American Journal of Mathematics},
      VOLUME = {111},
      YEAR = {1989},
      NUMBER = {1},
      PAGES = {111--134},
      ISSN = {0002-9327},
      CODEN = {AJMAAN},
      MRCLASS = {14H40 (14H10 14H30)},
      MRNUMBER = {90b:14035},
      DOI = {10.2307/2374482},
      ZBLNUMBER = {0699.14052},
      MRREVIEWER = {John B. Little},
      }
  • [ds] Go to document R. Donagi and R. C. Smith, "The structure of the Prym map," Acta Math., vol. 146, iss. 1-2, pp. 25-102, 1981.
    @article{ds, MRKEY = {594627},
      AUTHOR = {Donagi, Ron and Smith, Roy Campbell},
      TITLE = {The structure of the {P}rym map},
      JOURNAL = {Acta Math.},
      FJOURNAL = {Acta Mathematica},
      VOLUME = {146},
      YEAR = {1981},
      NUMBER = {1-2},
      PAGES = {25--102},
      ISSN = {0001-5962},
      CODEN = {ACMAA8},
      MRCLASS = {14H40 (14K30)},
      MRNUMBER = {82k:14030b},
      DOI = {10.1007/BF02392458},
      ZBLNUMBER = {0538.14019},
      MRREVIEWER = {V. V. Shokurov},
      }
  • [elbound] Go to document L. Ein and R. Lazarsfeld, "Singularities of theta divisors and the birational geometry of irregular varieties," J. Amer. Math. Society, vol. 10, iss. 1, pp. 243-258, 1997.
    @article{elbound, MRKEY = {1396893},
      AUTHOR = {Ein, Lawrence and Lazarsfeld, Robert},
      TITLE = {Singularities of theta divisors and the birational geometry of irregular varieties},
      JOURNAL = {J. Amer. Math. Society},
      FJOURNAL = {Journal of the American Mathematical Society},
      VOLUME = {10},
      YEAR = {1997},
      NUMBER = {1},
      PAGES = {243--258},
      ISSN = {0894-0347},
      MRCLASS = {14K05 (14E05)},
      MRNUMBER = {97d:14063},
      DOI = {10.1090/S0894-0347-97-00223-3},
      ZBLNUMBER = {0901.14028},
      MRREVIEWER = {J{á}nos Koll{á}r},
      }
  • [fm] R. Friedman and J. W. Morgan, Smooth Four-Manifolds and Complex Surfaces, New York: Springer-Verlag, 1994.
    @book{fm, MRKEY = {1288304},
      AUTHOR = {Friedman, Robert and Morgan, John W.},
      TITLE = {Smooth Four-Manifolds and Complex Surfaces},
      SERIES = {Ergeb. Math.},
      NUMBER = {27},
      PUBLISHER = {Springer-Verlag},
      ADDRESS = {New York},
      YEAR = {1994},
      PAGES = {x+520},
      ISBN = {3-540-57058-6},
      MRCLASS = {57R57 (14D20 14J27 32J15 57R55)},
      MRNUMBER = {95m:57046},
      ZBLNUMBER = {0817.14017},
      MRREVIEWER = {Zhenbo Qin},
      }
  • [fs] Go to document R. Friedman and R. Smith, "The generic Torelli theorem for the Prym map," Invent. Math., vol. 67, iss. 3, pp. 473-490, 1982.
    @article{fs, MRKEY = {664116},
      AUTHOR = {Friedman, Robert and Smith, Roy},
      TITLE = {The generic {T}orelli theorem for the {P}rym map},
      JOURNAL = {Invent. Math.},
      FJOURNAL = {Inventiones Mathematicae},
      VOLUME = {67},
      YEAR = {1982},
      NUMBER = {3},
      PAGES = {473--490},
      ISSN = {0020-9910},
      CODEN = {INVMBH},
      MRCLASS = {14H10 (14H40 14K10)},
      MRNUMBER = {83i:14017},
      DOI = {10.1007/BF01398932},
      ZBLNUMBER = {0506.14042},
      MRREVIEWER = {Sampei Usui},
      }
  • [fulton] W. Fulton, Intersection theory, New York: Springer-Verlag, 1984.
    @book{fulton, MRKEY = {732620},
      AUTHOR = {Fulton, William},
      TITLE = {Intersection theory},
      SERIES = {Ergebnisse der Mathematik und ihrer Grenzgebiete (3)},
      NUMBER = {2},
      PUBLISHER = {Springer-Verlag},
      ADDRESS = {New York},
      YEAR = {1984},
      PAGES = {xi+470},
      ISBN = {3-540-12176-5},
      MRCLASS = {14C17 (14-02 14C40)},
      MRNUMBER = {85k:14004},
      ZBLNUMBER = {0541.14005},
      MRREVIEWER = {Werner Kleinert},
      }
  • [green] Go to document M. L. Green, "Quadrics of rank four in the ideal of a canonical curve," Invent. Math., vol. 75, iss. 1, pp. 85-104, 1984.
    @article{green, MRKEY = {728141},
      AUTHOR = {Green, M. L.},
      TITLE = {Quadrics of rank four in the ideal of a canonical curve},
      JOURNAL = {Invent. Math.},
      FJOURNAL = {Inventiones Mathematicae},
      VOLUME = {75},
      YEAR = {1984},
      NUMBER = {1},
      PAGES = {85--104},
      ISSN = {0020-9910},
      CODEN = {INVMBH},
      MRCLASS = {14H40 (14C20 14H10)},
      MRNUMBER = {85f:14028},
      DOI = {10.1007/BF01403092},
      ZBLNUMBER = {0542.14018},
      MRREVIEWER = {Ciro Ciliberto},
      }
  • [gh] P. Griffiths and J. Harris, Principles of Algebraic Geometry, New York: Wiley, 1978.
    @book{gh, MRKEY = {507725},
      AUTHOR = {Griffiths, Phillip and Harris, Joseph},
      TITLE = {Principles of Algebraic Geometry},
      INVNOTE = {Pure and Applied Mathematics},
      PUBLISHER = {Wiley},
      ADDRESS = {New York},
      YEAR = {1978},
      PAGES = {xii+813},
      ISBN = {0-471-32792-1},
      MRCLASS = {14-01},
      MRNUMBER = {80b:14001},
      ZBLNUMBER = {0408.14001},
      MRREVIEWER = {Gerhard Pfister},
      }
  • [EGA1] A. Grothendieck, "Éléments de géométrie algébrique, III: Étude cohomologique des faisceaux cohérents, I," Inst. Hautes Études Sci. Publ. Math., iss. 11, p. 167, 1961.
    @article{EGA1, MRKEY = {0217085},
      AUTHOR = {Grothendieck, A.},
      TITLE = {\'{E}léments de géométrie algébrique, {III}: \'{E}tude cohomologique des faisceaux cohérents, {I}},
      JOURNAL = {Inst. Hautes Études Sci. Publ. Math.},
      FJOURNAL = {Institut des Hautes Études Scientifiques. Publications Mathématiques},
      NUMBER = {11},
      YEAR = {1961},
      PAGES = {167},
      ISSN = {0073-8301},
      MRCLASS = {14.55},
      MRNUMBER = {36 \#177c},
      }
  • [EGA2] A. Grothendieck, "Éléments de géométrie algébrique, III: Étude cohomologique des faisceaux cohérents, II," Inst. Hautes Études Sci. Publ. Math., iss. 17, p. 91, 1963.
    @article{EGA2, MRKEY = {0163911},
      AUTHOR = {Grothendieck, A.},
      TITLE = {\'{E}léments de géométrie algébrique, {III}: \'{E}tude cohomologique des faisceaux cohérents, {II}},
      JOURNAL = {Inst. Hautes Études Sci. Publ. Math.},
      FJOURNAL = {Institut des Hautes Études Scientifiques. Publications Mathématiques},
      NUMBER = {17},
      YEAR = {1963},
      PAGES = {91},
      ISSN = {0073-8301},
      MRCLASS = {14.05},
      MRNUMBER = {29 \#1210},
      MRREVIEWER = {H. Hironaka},
      }
  • [hart] R. Hartshorne, Algebraic Geometry, New York: Springer-Verlag, 1977.
    @book{hart, MRKEY = {0463157},
      AUTHOR = {Hartshorne, Robin},
      TITLE = {Algebraic Geometry},
      SERIES = {Grad. Texts Math.},
      NUMBER = {52},
      PUBLISHER = {Springer-Verlag},
      ADDRESS = {New York},
      YEAR = {1977},
      PAGES = {xvi+496},
      ISBN = {0-387-90244-9},
      MRCLASS = {14-01},
      MRNUMBER = {57 \#3116},
      ZBLNUMBER = {0367.14001},
      MRREVIEWER = {Robert Speiser},
      }
  • [kempf] Go to document G. Kempf, "On the geometry of a theorem of Riemann," Ann. of Math., vol. 98, pp. 178-185, 1973.
    @article{kempf, MRKEY = {0349687},
      AUTHOR = {Kempf, George},
      TITLE = {On the geometry of a theorem of {R}iemann},
      JOURNAL = {Ann. of Math. },
      FJOURNAL = {Annals of Mathematics. Second Series},
      VOLUME = {98},
      YEAR = {1973},
      PAGES = {178--185},
      ISSN = {0003-486X},
      MRCLASS = {14H40 (14K25)},
      MRNUMBER = {50 \#2180},
      DOI = {10.2307/1970910},
      ZBLNUMBER = {0275.14023},
      MRREVIEWER = {H. H. Martens},
      }
  • [kbound] J. Kollár, Shafarevich Maps and Automorphic Forms, Princeton, NJ: Princeton University Press, 1995.
    @book{kbound, MRKEY = {1341589},
      AUTHOR = {Koll{á}r, J{á}nos},
      TITLE = {Shafarevich {M}aps and {A}utomorphic {F}orms},
      INVSERIES = {M. B. Porter Lectures},
      PUBLISHER = {Princeton University Press},
      ADDRESS = {Princeton, NJ},
      YEAR = {1995},
      PAGES = {x+201},
      ISBN = {0-691-04381-7},
      MRCLASS = {14E20 (14J10 14J15 32J18 32N10)},
      MRNUMBER = {96i:14016},
      ZBLNUMBER = {0871.14015},
      MRREVIEWER = {Kang Zuo},
      }
  • [martens] H. H. Martens, "On the varieties of special divisors on a curve," J. Reine Angew. Math., vol. 227, pp. 111-120, 1967.
    @article{martens, MRKEY = {0215847},
      AUTHOR = {Martens, Henrik H.},
      TITLE = {On the varieties of special divisors on a curve},
      JOURNAL = {J. Reine Angew. Math.},
      FJOURNAL = {Journal für die Reine und Angewandte Mathematik},
      VOLUME = {227},
      YEAR = {1967},
      PAGES = {111--120},
      ISSN = {0075-4102},
      MRCLASS = {14.20},
      MRNUMBER = {35 \#6682},
      ZBLNUMBER = {0172.46301},
      MRREVIEWER = {P. Du Val},
      }
  • [miranda] R. Miranda, Algebraic curves and Riemann surfaces, Providence, RI: American Mathematical Society, 1995.
    @book{miranda, MRKEY = {1326604},
      AUTHOR = {Miranda, Rick},
      TITLE = {Algebraic curves and {R}iemann surfaces},
      SERIES = {Graduate Studies in Math.},
      NUMBER = {5},
      PUBLISHER = {American Mathematical Society},
      ADDRESS = {Providence, RI},
      YEAR = {1995},
      PAGES = {xxii+390},
      ISBN = {0-8218-0268-2},
      MRCLASS = {14Hxx (14-01 30F99)},
      MRNUMBER = {96f:14029},
      ZBLNUMBER = {0820.14022},
      MRREVIEWER = {R. F. Lax},
      }
  • [mumab] D. Mumford, Abelian Varieties, Mumbai: Tata Institute of Fundamental Research, 1970.
    @book{mumab, MRKEY = {0282985},
      AUTHOR = {Mumford, David},
      TITLE = {Abelian {V}arieties},
      SERIES = {Studies in Math.},
      NUMBER = {5},
      FSERIES = {Tata Institute of Fundamental Research Studies in Mathematics, No. 5 },
      PUBLISHER = {Tata Institute of Fundamental Research},
      ADDRESS = {Mumbai},
      YEAR = {1970},
      PAGES = {viii+242},
      MRCLASS = {14.51},
      MRNUMBER = {44 \#219},
      ZBLNUMBER = {0223.14022},
      MRREVIEWER = {J. S. Milne},
      }
  • [mum1] D. Mumford, "Prym varieties, I," in Contributions to Analysis: A Collection of Papers Dedicated to Lipman Bers, Ahlfors, L. V., Kra, I., Maskit, B., and Nirenberg, L., Eds., New York: Academic Press, 1974, pp. 325-350.
    @incollection{mum1, MRKEY = {0379510},
      AUTHOR = {Mumford, David},
      EDITOR = {Ahlfors, Lars V. and Kra, Irwin and Maskit, Bernard and Nirenberg, Louis},
      TITLE = {Prym varieties, {I}},
      BOOKTITLE = {Contributions to {A}nalysis: {A} {C}ollection of {P}apers {D}edicated to {L}ipman {B}ers},
      PAGES = {325--350},
      PUBLISHER = {Academic Press},
      ADDRESS = {New York},
      YEAR = {1974},
      MRCLASS = {14H40 (14K25 32G20)},
      MRNUMBER = {52 \#415},
      ZBLNUMBER = {0299.14018},
      MRREVIEWER = {H. H. Martens},
      }
  • [svbound] Go to document R. Smith and R. Varley, "Multiplicity $g$ points on theta divisors," Duke Math. J., vol. 82, iss. 2, pp. 319-326, 1996.
    @article{svbound, MRKEY = {1387231},
      AUTHOR = {Smith, Roy and Varley, Robert},
      TITLE = {Multiplicity {$g$} points on theta divisors},
      JOURNAL = {Duke Math. J.},
      FJOURNAL = {Duke Mathematical Journal},
      VOLUME = {82},
      YEAR = {1996},
      NUMBER = {2},
      PAGES = {319--326},
      ISSN = {0012-7094},
      CODEN = {DUMJAO},
      MRCLASS = {14K05 (14H40)},
      MRNUMBER = {97c:14043},
      DOI = {10.1215/S0012-7094-96-08214-9},
      ZBLNUMBER = {0903.14017},
      MRREVIEWER = {H. Lange},
      }
  • [sv1] R. Smith and R. Varley, "A Riemann singularities theorem for Prym theta divisors, with applications," Pacific J. Math., vol. 201, iss. 2, pp. 479-509, 2001.
    @article{sv1, MRKEY = {1875904},
      AUTHOR = {Smith, Roy and Varley, Robert},
      TITLE = {A {R}iemann singularities theorem for {P}rym theta divisors, with applications},
      JOURNAL = {Pacific J. Math.},
      FJOURNAL = {Pacific Journal of Mathematics},
      VOLUME = {201},
      YEAR = {2001},
      NUMBER = {2},
      PAGES = {479--509},
      ISSN = {0030-8730},
      CODEN = {PJMAAI},
      MRCLASS = {14H40 (14C34)},
      MRNUMBER = {2003d:14039},
      ZBLNUMBER = {1065.14037},
      MRREVIEWER = {Esteban G{ó}mez Gonz{á}lez},
      }
  • [sv3] R. Smith and R. Varley, "The Prym Torelli problem: An update and a reformulation as a question in birational geometry," in Symposium in Honor of C. H. Clemens, Bertram, A., Carlson, J. A., and Kley, H., Eds., Providence, RI: Amer. Math. Soc., 2002, pp. 235-264.
    @incollection{sv3, MRKEY = {1941584},
      AUTHOR = {Smith, R. and Varley, R.},
      EDITOR = {Bertram, Aaron and Carlson, James A. and Kley, Holger},
      TITLE = {The {P}rym {T}orelli problem: {A}n update and a reformulation as a question in birational geometry},
      BOOKTITLE = {Symposium in {H}onor of {C}. {H}. {C}lemens},
      VENUE = {Salt Lake City, 2000},
      SERIES = {Contemp. Math.},
      NUMBER = {312},
      PAGES = {235--264},
      PUBLISHER = {Amer. Math. Soc.},
      ADDRESS = {Providence, RI},
      YEAR = {2002},
      MRCLASS = {14C34 (14H40 14H42 14K30)},
      MRNUMBER = {2003j:14011},
      ZBLNUMBER = {1058.14016},
      MRREVIEWER = {V. V. Chueshev},
      }
  • [sv2] Go to document R. Smith and R. Varley, "A necessary and sufficient condition for Riemann’s singularity theorem to hold on a Prym theta divisor," Compos. Math., vol. 140, iss. 2, pp. 447-458, 2004.
    @article{sv2, MRKEY = {2027198},
      AUTHOR = {Smith, Roy and Varley, Robert},
      TITLE = {A necessary and sufficient condition for {R}iemann's singularity theorem to hold on a {P}rym theta divisor},
      JOURNAL = {Compos. Math.},
      FJOURNAL = {Compositio Mathematica},
      VOLUME = {140},
      YEAR = {2004},
      NUMBER = {2},
      PAGES = {447--458},
      ISSN = {0010-437X},
      MRCLASS = {14H40},
      MRNUMBER = {2005b:14059},
      DOI = {10.1112/S0010437X03000320},
      ZBLNUMBER = {1071.14031},
      MRREVIEWER = {Samwel Dalalyan},
      }
  • [t] A. N. Tjurin, "The geometry of the Poincaré divisor of a Prym variety," Izv. Akad. Nauk SSSR Ser. Mat., vol. 39, iss. 5, pp. 1003-1043, 1219, 1975.
    @article{t, MRKEY = {0414563},
      AUTHOR = {Tjurin, A. N.},
      TITLE = {The geometry of the {P}oincaré divisor of a {P}rym variety},
      JOURNAL = {Izv. Akad. Nauk SSSR Ser. Mat.},
      FJOURNAL = {Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya},
      VOLUME = {39},
      YEAR = {1975},
      NUMBER = {5},
      PAGES = {1003--1043, 1219},
      NOTE = {In Russian; translated in {\it Math. USSR-Izv.} {\bf 9} (1975), 951--986; corrected in {\bf 12} (1978), 438},
      ISSN = {0373-2436},
      MRCLASS = {14H40 (14K25 14H30)},
      MRNUMBER = {54 \#2664},
      MRREVIEWER = {P. E. Newstead},
      }

Authors

Sebastian Casalaina-Martin

Department of Mathematics
Columbia University
New York, NY 10027
United States