Abstract
We show that the number of birational automorphisms of a variety of general type $X$ is bounded by $c \cdot \mathrm{vol}(X,K_X)$, where $c$ is a constant that only depends on the dimension of $X$.
-
[Alexeev94]
V. Alexeev, "Boundedness and $K^2$ for log surfaces," Internat. J. Math., vol. 5, iss. 6, pp. 779-810, 1994.
@article {Alexeev94, MRKEY = {1298994},
AUTHOR = {Alexeev, Valery},
TITLE = {Boundedness and {$K\sp 2$} for log surfaces},
JOURNAL = {Internat. J. Math.},
FJOURNAL = {International Journal of Mathematics},
VOLUME = {5},
YEAR = {1994},
NUMBER = {6},
PAGES = {779--810},
ISSN = {0129-167X},
MRCLASS = {14J10 (14J25)},
MRNUMBER = {1298994},
MRREVIEWER = {Mark Gross},
DOI = {10.1142/S0129167X94000395},
ZBLNUMBER = {0838.14028},
} -
[AM04]
V. Alexeev and S. Mori, "Bounding singular surfaces of general type," in Algebra, Arithmetic and Geometry with Applications, New York: Springer-Verlag, 2004, pp. 143-174.
@incollection {AM04, MRKEY = {2037085},
AUTHOR = {Alexeev, Valery and Mori, Shigefumi},
TITLE = {Bounding singular surfaces of general type},
BOOKTITLE = {Algebra, Arithmetic and Geometry with Applications},
VENUE={{W}est {L}afayette, {IN},
2000},
PAGES = {143--174},
PUBLISHER = {Springer-Verlag},
ADDRESS = {New York},
YEAR = {2004},
MRCLASS = {14J29},
MRNUMBER = {2037085},
MRREVIEWER = {S{á}ndor J. Kov{á}cs},
ZBLNUMBER = {1103.14021},
DOI = {10.1007/978-3-642-18487-1_7},
} -
[Andreotti50] A. Andreotti, "Sopra le superficie algebriche che posseggono trasformazioni birazionali in sè," Univ. Roma Ist. Naz. Alta Mat. Rend. Mat. e Appl., vol. 9, pp. 255-279, 1950.
@article {Andreotti50, MRKEY = {0049601},
AUTHOR = {Andreotti, Aldo},
TITLE = {Sopra le superficie algebriche che posseggono trasformazioni birazionali in sè},
JOURNAL = {Univ. Roma Ist. Naz. Alta Mat. Rend. Mat. e Appl.},
VOLUME = {9},
YEAR = {1950},
PAGES = {255--279},
MRCLASS = {14.0X},
MRNUMBER = {0049601},
MRREVIEWER = {J. A. Todd},
ZBLNUMBER = {0041.08502},
} -
[AS95]
U. Angehrn and Y. T. Siu, "Effective freeness and point separation for adjoint bundles," Invent. Math., vol. 122, iss. 2, pp. 291-308, 1995.
@article {AS95, MRKEY = {1358978},
AUTHOR = {Angehrn, Urban and Siu, Yum Tong},
TITLE = {Effective freeness and point separation for adjoint bundles},
JOURNAL = {Invent. Math.},
FJOURNAL = {Inventiones Mathematicae},
VOLUME = {122},
YEAR = {1995},
NUMBER = {2},
PAGES = {291--308},
ISSN = {0020-9910},
CODEN = {INVMBH},
MRCLASS = {32J25 (14C20 32L10)},
MRNUMBER = {1358978},
MRREVIEWER = {Jaros{\l}aw A. Wi{\'s}niewski},
DOI = {10.1007/BF01231446},
ZBLNUMBER = {0847.32035},
} -
[Ballico93] E. Ballico, "On the automorphisms of surfaces of general type in positive characteristic," Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei Mat. Appl., vol. 4, iss. 2, pp. 121-129, 1993.
@article {Ballico93, MRKEY = {1233400},
AUTHOR = {Ballico, Edoardo},
TITLE = {On the automorphisms of surfaces of general type in positive characteristic},
JOURNAL = {Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei Mat. Appl.},
FJOURNAL = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Serie IX. Matematica e Applicazioni},
VOLUME = {4},
YEAR = {1993},
NUMBER = {2},
PAGES = {121--129},
ISSN = {1120-6330},
MRCLASS = {14J29 (14E09)},
MRNUMBER = {1233400},
MRREVIEWER = {Yoichi Miyaoka},
ZBLNUMBER = {0795.14022},
} -
[BP10]
B. Berndtsson and M. Puaun, "Quantitative extensions of pluricanonical forms and closed positive currents," Nagoya Math. J., vol. 205, pp. 25-65, 2012.
@article {BP10, MRKEY = {2891164},
AUTHOR = {Berndtsson, Bo and P{\u{a}}un, Mihai},
TITLE = {Quantitative extensions of pluricanonical forms and closed positive currents},
JOURNAL = {Nagoya Math. J.},
FJOURNAL = {Nagoya Mathematical Journal},
VOLUME = {205},
YEAR = {2012},
PAGES = {25--65},
ISSN = {0027-7630},
MRCLASS = {32Q15 (14D07 32U40)},
MRNUMBER = {2891164},
MRREVIEWER = {James McKernan},
URL = {http://projecteuclid.org/euclid.nmj/1330611001},
ZBLNUMBER = {1248.32012},
} -
[BCHM06]
C. Birkar, P. Cascini, C. D. Hacon, and J. McKernan, "Existence of minimal models for varieties of log general type," J. Amer. Math. Soc., vol. 23, iss. 2, pp. 405-468, 2010.
@article {BCHM06, MRKEY = {2601039},
AUTHOR = {Birkar, Caucher and Cascini, Paolo and Hacon, Christopher D. and McKernan, James},
TITLE = {Existence of minimal models for varieties of log general type},
JOURNAL = {J. Amer. Math. Soc.},
FJOURNAL = {Journal of the American Mathematical Society},
VOLUME = {23},
YEAR = {2010},
NUMBER = {2},
PAGES = {405--468},
ISSN = {0894-0347},
MRCLASS = {14E30 (14E05)},
MRNUMBER = {2601039},
MRREVIEWER = {Mark Gross},
DOI = {10.1090/S0894-0347-09-00649-3},
ZBLNUMBER = {1210.14019},
} -
[Cai00]
J. Cai, "Bounds of automorphisms of surfaces of general type in positive characteristic," J. Pure Appl. Algebra, vol. 149, iss. 3, pp. 241-250, 2000.
@article {Cai00, MRKEY = {1762766},
AUTHOR = {Cai, Jin-Xing},
TITLE = {Bounds of automorphisms of surfaces of general type in positive characteristic},
JOURNAL = {J. Pure Appl. Algebra},
FJOURNAL = {Journal of Pure and Applied Algebra},
VOLUME = {149},
YEAR = {2000},
NUMBER = {3},
PAGES = {241--250},
ISSN = {0022-4049},
CODEN = {JPAAA2},
MRCLASS = {14J50 (14H37 14J29)},
MRNUMBER = {1762766},
MRREVIEWER = {Miguel A. Barja},
DOI = {10.1016/S0022-4049(99)00064-X},
ZBLNUMBER = {0968.14023},
} -
[CS95]
F. Catanese and M. Schneider, "Polynomial bounds for abelian groups of automorphisms," Compositio Math., vol. 97, iss. 1-2, pp. 1-15, 1995.
@article {CS95, MRKEY = {1355114},
AUTHOR = {Catanese, Fabrizio and Schneider, Michael},
TITLE = {Polynomial bounds for abelian groups of automorphisms},
NOTE = {Special issue in honour of Frans Oort},
JOURNAL = {Compositio Math.},
FJOURNAL = {Compositio Mathematica},
VOLUME = {97},
YEAR = {1995},
NUMBER = {1-2},
PAGES = {1--15},
ISSN = {0010-437X},
CODEN = {CMPMAF},
MRCLASS = {14L30 (14E09)},
MRNUMBER = {1355114},
MRREVIEWER = {P. Abellanas},
URL = {http://www.numdam.org/item?id=CM_1995__97_1-2_1_0},
ZBLNUMBER = {0858.14008},
} -
[Corti91]
A. Corti, "Polynomial bounds for the number of automorphisms of a surface of general type," Ann. Sci. École Norm. Sup., vol. 24, iss. 1, pp. 113-137, 1991.
@article {Corti91, MRKEY = {1088272},
AUTHOR = {Corti, Alessio},
TITLE = {Polynomial bounds for the number of automorphisms of a surface of general type},
JOURNAL = {Ann. Sci. École Norm. Sup.},
FJOURNAL = {Annales Scientifiques de l'École Normale Supérieure. Quatrième Série},
VOLUME = {24},
YEAR = {1991},
NUMBER = {1},
PAGES = {113--137},
ISSN = {0012-9593},
CODEN = {ASENAH},
MRCLASS = {14J50 (14J29)},
MRNUMBER = {1088272},
MRREVIEWER = {Jong Hae Keum},
URL = {http://www.numdam.org/item?id=ASENS_1991_4_24_1_113_0},
ZBLNUMBER = {0758.14026},
} -
[FH11]
T. de Fernex and C. D. Hacon, "Deformations of canonical pairs and Fano varieties," J. Reine Angew. Math., vol. 651, pp. 97-126, 2011.
@article {FH11, MRKEY = {2774312},
AUTHOR = {de Fernex, Tommaso and Hacon, Christopher D.},
TITLE = {Deformations of canonical pairs and {F}ano varieties},
JOURNAL = {J. Reine Angew. Math.},
FJOURNAL = {Journal für die Reine und Angewandte Mathematik. [Crelle's Journal]},
VOLUME = {651},
YEAR = {2011},
PAGES = {97--126},
ISSN = {0075-4102},
CODEN = {JRMAA8},
MRCLASS = {14E30 (14J45)},
MRNUMBER = {2774312},
MRREVIEWER = {Anne-Sophie Kaloghiros},
DOI = {10.1515/CRELLE.2011.010},
ZBLNUMBER = {1220.14026},
} -
[Fulton93] W. Fulton, Introduction to Toric Varieties, Princeton, NJ: Princeton Univ. Press, 1993, vol. 131.
@book {Fulton93, MRKEY = {1234037},
AUTHOR = {Fulton, William},
TITLE = {Introduction to Toric Varieties},
SERIES = {Annals of Math. Studies},
VOLUME = {131},
PUBLISHER = {Princeton Univ. Press},
ADDRESS = {Princeton, NJ},
YEAR = {1993},
PAGES = {xii+157},
ISBN = {0-691-00049-2},
MRCLASS = {14M25 (14-02 14J30)},
MRNUMBER = {1234037},
MRREVIEWER = {T. Oda},
ZBLNUMBER = {0813.14039},
} -
[GLS94] D. Gorenstein, R. Lyons, and R. Solomon, The Classification of the Finite Simple Groups, Providence, RI: Amer. Math. Soc., 1994, vol. 40.
@book {GLS94, MRKEY = {1303592},
AUTHOR = {Gorenstein, Daniel and Lyons, Richard and Solomon, Ronald},
TITLE = {The Classification of the Finite Simple Groups},
SERIES = {Math. Surveys Monogr.},
VOLUME = {40},
PUBLISHER = {Amer. Math. Soc.},
ADDRESS = {Providence, RI},
YEAR = {1994},
PAGES = {xiv+165},
ISBN = {0-8218-0334-4},
MRCLASS = {20D05 (20-02)},
MRNUMBER = {1303592},
MRREVIEWER = {J. L. Alperin},
ZBLNUMBER = {0816.20016},
} -
[EGAIV]
A. Grothendieck, "Eléménts de Géométrie Algébrique. IV," Publ. Math. IHES, vol. 28, pp. 5-255, 1966.
@article{EGAIV, MRKEY={0217086},
AUTHOR={Grothendieck, A.},
TITLE={Eléménts de Géométrie Algébrique. {IV}},
JOURNAL={Publ. Math. IHES},
VOLUME={28},
YEAR={1966},
PAGES={5--255},
ZBLNUMBER = {0144.19904},
MRNUMBER = {0217086},
URL = {http://www.numdam.org/item?id=PMIHES_1966__28__5_0},
} -
[HM05b]
C. D. Hacon and J. McKernan, "Boundedness of pluricanonical maps of varieties of general type," Invent. Math., vol. 166, iss. 1, pp. 1-25, 2006.
@article {HM05b, MRKEY = {2242631},
AUTHOR = {Hacon, Christopher D. and McKernan, James},
TITLE = {Boundedness of pluricanonical maps of varieties of general type},
JOURNAL = {Invent. Math.},
FJOURNAL = {Inventiones Mathematicae},
VOLUME = {166},
YEAR = {2006},
NUMBER = {1},
PAGES = {1--25},
ISSN = {0020-9910},
CODEN = {INVMBH},
MRCLASS = {14E05 (14J40)},
MRNUMBER = {2242631},
MRREVIEWER = {Meng Chen},
DOI = {10.1007/s00222-006-0504-1},
ZBLNUMBER = {1121.14011},
} -
[HS91]
A. T. Huckleberry and M. Sauer, "On the order of the automorphism group of a surface of general type," Math. Z., vol. 205, iss. 2, pp. 321-329, 1990.
@article {HS91, MRKEY = {1076138},
AUTHOR = {Huckleberry, A. T. and Sauer, M.},
TITLE = {On the order of the automorphism group of a surface of general type},
JOURNAL = {Math. Z.},
FJOURNAL = {Mathematische Zeitschrift},
VOLUME = {205},
YEAR = {1990},
NUMBER = {2},
PAGES = {321--329},
ISSN = {0025-5874},
CODEN = {MAZEAX},
MRCLASS = {14J50 (14J29)},
MRNUMBER = {1076138},
MRREVIEWER = {Jong Hae Keum},
DOI = {10.1007/BF02571245},
ZBLNUMBER = {0718.32022},
} -
[Kollar92b]
J. Kollár, "Log surfaces of general type; some conjectures," in Classification of Algebraic Varieties, Providence, RI: Amer. Math. Soc., 1994, vol. 162, pp. 261-275.
@incollection {Kollar92b, MRKEY = {1272703},
AUTHOR = {Koll{á}r, J{á}nos},
TITLE = {Log surfaces of general type; some conjectures},
BOOKTITLE = {Classification of Algebraic Varieties},
VENUE={{L}'{A}quila, 1992},
SERIES = {Contemp. Math.},
VOLUME = {162},
PAGES = {261--275},
PUBLISHER = {Amer. Math. Soc.},
ADDRESS = {Providence, RI},
YEAR = {1994},
MRCLASS = {14J29 (14E05)},
MRNUMBER = {1272703},
MRREVIEWER = {Gang Xiao},
DOI = {10.1090/conm/162/01538},
ZBLNUMBER = {0860.14014},
} -
[Kollar95] J. Kollár, "Singularities of pairs," in Algebraic Geometry—Santa Cruz 1995, Providence, RI: Amer. Math. Soc., 1997, vol. 62, pp. 221-287.
@incollection {Kollar95, MRKEY = {1492525},
AUTHOR = {Koll{á}r, J{á}nos},
TITLE = {Singularities of pairs},
BOOKTITLE = {Algebraic Geometry---{S}anta {C}ruz 1995},
SERIES = {Proc. Sympos. Pure Math.},
VOLUME = {62},
PAGES = {221--287},
PUBLISHER = {Amer. Math. Soc.},
ADDRESS = {Providence, RI},
YEAR = {1997},
MRCLASS = {14E30 (14E15 32S40)},
MRNUMBER = {1492525},
MRREVIEWER = {Alessio Corti},
ZBLNUMBER = {0905.14002},
} -
[Kollar08]
J. Kollár, "Is there a topological Bogomolov-Miyaoka-Yau inequality?," Pure Appl. Math. Q., vol. 4, pp. 203-236, 2008.
@article {Kollar08, MRKEY = {2400877},
AUTHOR = {Koll{á}r, J{á}nos},
TITLE = {Is there a topological {B}ogomolov-{M}iyaoka-{Y}au inequality?},
JOURNAL = {Pure Appl. Math. Q.},
FJOURNAL = {Pure and Applied Mathematics Quarterly},
VOLUME = {4},
YEAR = {2008},
PAGES = {203--236},
ISSN = {1558-8599},
MRCLASS = {14J80 (14J17 57N13)},
MRNUMBER = {2400877},
MRREVIEWER = {Arnaud Beauville},
ZBLNUMBER = {1145.14031},
DOI = {10.1090/pspum/062.1/1492525},
} -
[KM98]
J. Kollár and S. Mori, Birational Geometry of Algebraic Varieties, Cambridge: Cambridge Univ. Press, 1998, vol. 134.
@book {KM98, MRKEY = {1658959},
AUTHOR = {Koll{á}r, J{á}nos and Mori, Shigefumi},
TITLE = {Birational Geometry of Algebraic Varieties},
SERIES = {Cambridge Tracts in Math.},
VOLUME = {134},
PUBLISHER = {Cambridge Univ. Press},
ADDRESS = {Cambridge},
YEAR = {1998},
PAGES = {viii+254},
ISBN = {0-521-63277-3},
MRCLASS = {14E30},
MRNUMBER = {1658959},
MRREVIEWER = {Mark Gross},
DOI = {10.1017/CBO9780511662560},
ZBLNUMBER = {0926.14003},
} -
[Lazarsfeld04b] R. Lazarsfeld, Positivity in Algebraic Geometry. II, New York: Springer-Verlag, 2004, vol. 49.
@book {Lazarsfeld04b, MRKEY = {2095472},
AUTHOR = {Lazarsfeld, Robert},
TITLE = {Positivity in Algebraic Geometry. {II}},
SERIES = {Ergeb. Math. Grenzgeb.},
VOLUME = {49},
NOTE = {Positivity for vector bundles, and multiplier ideals},
PUBLISHER = {Springer-Verlag},
ADDRESS = {New York},
YEAR = {2004},
PAGES = {xviii+385},
ISBN = {3-540-22534-X},
MRCLASS = {14-02 (14C20 14F05 14F17)},
MRNUMBER = {2095472},
MRREVIEWER = {Mihnea Popa},
ZBLNUMBER = {1093.14500},
} -
[Matsumura63] H. Matsumura, "On algebraic groups of birational transformations," Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur., vol. 34, pp. 151-155, 1963.
@article {Matsumura63, MRKEY = {0159825},
AUTHOR = {Matsumura, Hideyuki},
TITLE = {On algebraic groups of birational transformations},
JOURNAL = {Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur.},
FJOURNAL = {Atti della Accademia Nazionale dei Lincei. Rendiconti. Classe di Scienze Fisiche, Matematiche e Naturali},
VOLUME = {34},
YEAR = {1963},
PAGES = {151--155},
MRCLASS = {14.15},
MRNUMBER = {0159825},
MRREVIEWER = {P. Cartier},
ZBLNUMBER = {0134.16601},
} -
[Nakayama04] N. Nakayama, Zariski-Decomposition and Abundance, Tokyo: Mathematical Society of Japan, 2004, vol. 14.
@book {Nakayama04, MRKEY = {2104208},
AUTHOR = {Nakayama, Noboru},
TITLE = {Zariski-Decomposition and Abundance},
SERIES = {MSJ Memoirs},
VOLUME = {14},
PUBLISHER = {Mathematical Society of Japan},
ADDRESS = {Tokyo},
YEAR = {2004},
PAGES = {xiv+277},
ISBN = {4-931469-31-0},
MRCLASS = {14C20 (14E15 14E30 14J10)},
MRNUMBER = {2104208},
MRREVIEWER = {Tommaso De Fernex},
ZBLNUMBER = {1061.14018},
} -
@article {Siu98, MRKEY = {1660941},
AUTHOR = {Siu, Yum-Tong},
TITLE = {Invariance of plurigenera},
JOURNAL = {Invent. Math.},
FJOURNAL = {Inventiones Mathematicae},
VOLUME = {134},
YEAR = {1998},
NUMBER = {3},
PAGES = {661--673},
ISSN = {0020-9910},
CODEN = {INVMBH},
MRCLASS = {32L10 (32G13 32J18)},
MRNUMBER = {1660941},
MRREVIEWER = {J{á}nos Koll{á}r},
DOI = {10.1007/s002220050276},
ZBLNUMBER = {0955.32017},
} -
[Stichtenoth73] H. Stichtenoth, "Über die Automorphismengruppe eines algebraischen Funktionenkörpers von Primzahlcharakteristik. I. Eine Abschätzung der Ordnung der Automorphismengruppe," Arch. Math. $($Basel$)$, vol. 24, pp. 527-544, 1973.
@article {Stichtenoth73, MRKEY = {0337980},
AUTHOR = {Stichtenoth, Henning},
TITLE = {Über die {A}utomorphismengruppe eines algebraischen {F}unktionenkörpers von {P}rimzahlcharakteristik. {I}. {E}ine {A}bschätzung der {O}rdnung der {A}utomorphismengruppe},
JOURNAL = {Arch. Math. $($Basel$)$},
FJOURNAL = {Archiv der Mathematik},
VOLUME = {24},
YEAR = {1973},
PAGES = {527--544},
ISSN = {0003-889X},
MRCLASS = {14H05},
MRNUMBER = {0337980},
MRREVIEWER = {W.-D. Geyer},
ZBLNUMBER = {0282.14007},
} -
[Szabo96]
E. Szabó, "Bounding automorphism groups," Math. Ann., vol. 304, iss. 4, pp. 801-811, 1996.
@article {Szabo96, MRKEY = {1380456},
AUTHOR = {Szab{ó},
Endre},
TITLE = {Bounding automorphism groups},
JOURNAL = {Math. Ann.},
FJOURNAL = {Mathematische Annalen},
VOLUME = {304},
YEAR = {1996},
NUMBER = {4},
PAGES = {801--811},
ISSN = {0025-5831},
CODEN = {MAANA},
MRCLASS = {14J50 (14E09)},
MRNUMBER = {1380456},
MRREVIEWER = {Alessio Corti},
DOI = {10.1007/BF01446320},
ZBLNUMBER = {0845.14009},
} -
[Takayama06]
S. Takayama, "Pluricanonical systems on algebraic varieties of general type," Invent. Math., vol. 165, iss. 3, pp. 551-587, 2006.
@article {Takayama06, MRKEY = {2242627},
AUTHOR = {Takayama, Shigeharu},
TITLE = {Pluricanonical systems on algebraic varieties of general type},
JOURNAL = {Invent. Math.},
FJOURNAL = {Inventiones Mathematicae},
VOLUME = {165},
YEAR = {2006},
NUMBER = {3},
PAGES = {551--587},
ISSN = {0020-9910},
CODEN = {INVMBH},
MRCLASS = {14E05 (14C20 14J40)},
MRNUMBER = {2242627},
MRREVIEWER = {Tomasz Szemberg},
DOI = {10.1007/s00222-006-0503-2},
ZBLNUMBER = {1108.14031},
} -
[Tsuji00] H. Tsuji, Bound of automorphisms of projective varieties of general type.
@misc{Tsuji00,
author = {Tsuji, Hajime},
TITLE = {Bound of automorphisms of projective varieties of general type},
ARXIV = {math/0004138},
SORTYEAR={2014},
} -
[Tsuji07]
H. Tsuji, "Pluricanonical systems of projective varieties of general type. II," Osaka J. Math., vol. 44, iss. 3, pp. 723-764, 2007.
@article {Tsuji07, MRKEY = {2360948},
AUTHOR = {Tsuji, Hajime},
TITLE = {Pluricanonical systems of projective varieties of general type. {II}},
JOURNAL = {Osaka J. Math.},
FJOURNAL = {Osaka Journal of Mathematics},
VOLUME = {44},
YEAR = {2007},
NUMBER = {3},
PAGES = {723--764},
ISSN = {0030-6126},
CODEN = {OJMAA7},
MRCLASS = {14E30 (14J40 32J18 32L10)},
MRNUMBER = {2360948},
MRREVIEWER = {Gianluca Occhetta},
URL = {http://projecteuclid.org/euclid.ojm/1189717430},
ZBLNUMBER = {1186.14043},
} -
[Xiao94]
G. Xiao, "Bound of automorphisms of surfaces of general type. I," Ann. of Math., vol. 139, iss. 1, pp. 51-77, 1994.
@article {Xiao94, MRKEY = {1259364},
AUTHOR = {Xiao, Gang},
TITLE = {Bound of automorphisms of surfaces of general type. {I}},
JOURNAL = {Ann. of Math.},
FJOURNAL = {Annals of Mathematics. Second Series},
VOLUME = {139},
YEAR = {1994},
NUMBER = {1},
PAGES = {51--77},
ISSN = {0003-486X},
CODEN = {ANMAAH},
MRCLASS = {14J50 (14J29)},
MRNUMBER = {1259364},
MRREVIEWER = {Sonny Tendian},
DOI = {10.2307/2946627},
ZBLNUMBER = {0811.14011},
} -
[Xiao95] G. Xiao, "Bound of automorphisms of surfaces of general type. II," J. Algebraic Geom., vol. 4, iss. 4, pp. 701-793, 1995.
@article {Xiao95, MRKEY = {1339845},
AUTHOR = {Xiao, Gang},
TITLE = {Bound of automorphisms of surfaces of general type. {II}},
JOURNAL = {J. Algebraic Geom.},
FJOURNAL = {Journal of Algebraic Geometry},
VOLUME = {4},
YEAR = {1995},
NUMBER = {4},
PAGES = {701--793},
ISSN = {1056-3911},
MRCLASS = {14J50 (14J29)},
MRNUMBER = {1339845},
MRREVIEWER = {Kang Zuo},
ZBLNUMBER = {0841.14011},
} -
[Xiao96]
G. Xiao, "Linear bound for abelian automorphisms of varieties of general type," J. Reine Angew. Math., vol. 476, pp. 201-207, 1996.
@article {Xiao96, MRKEY = {1401701},
AUTHOR = {Xiao, Gang},
TITLE = {Linear bound for abelian automorphisms of varieties of general type},
JOURNAL = {J. Reine Angew. Math.},
FJOURNAL = {Journal für die Reine und Angewandte Mathematik. [Crelle's Journal]},
VOLUME = {476},
YEAR = {1996},
PAGES = {201--207},
ISSN = {0075-4102},
CODEN = {JRMAA8},
MRCLASS = {14J50},
MRNUMBER = {1401701},
MRREVIEWER = {P. Abellanas},
DOI = {10.1515/crll.1996.476.201},
ZBLNUMBER = {0870.14006},
} -
[Zhang07]
D. Zhang, "Small bound for birational automorphism groups of algebraic varieties," Math. Ann., vol. 339, iss. 4, pp. 957-975, 2007.
@article {Zhang07, MRKEY = {2341909},
AUTHOR = {Zhang, De-Qi},
TITLE = {Small bound for birational automorphism groups of algebraic varieties},
NOTE = {with an appendix by Yujiro Kawamata},
JOURNAL = {Math. Ann.},
FJOURNAL = {Mathematische Annalen},
VOLUME = {339},
YEAR = {2007},
NUMBER = {4},
PAGES = {957--975},
ISSN = {0025-5831},
CODEN = {MAANA},
MRCLASS = {14J50 (14E07)},
MRNUMBER = {2341909},
MRREVIEWER = {Massimiliano Mella},
DOI = {10.1007/s00208-007-0162-7},
ZBLNUMBER = {1128.14029},
}