Abstract
Generalized complex geometry encompasses complex and symplectic geometry as its extremal special cases. We explore the basic properties of this geometry, including its enhanced symmetry group, elliptic deformation theory, relation to Poisson geometry, and local structure theory. We also define and study generalized complex branes, which interpolate between flat bundles on Lagrangian submanifolds and holomorphic bundles on complex submanifolds.
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@article {abo, MRKEY = {2240211},
AUTHOR = {Abouzaid, Mohammed and Boyarchenko, Mitya},
TITLE = {Local structure of generalized complex manifolds},
JOURNAL = {J. Symplectic Geom.},
FJOURNAL = {The Journal of Symplectic Geometry},
VOLUME = {4},
YEAR = {2006},
NUMBER = {1},
PAGES = {43--62},
ISSN = {1527-5256},
MRCLASS = {53D17 (53C10)},
MRNUMBER = {2240211},
MRREVIEWER = {Yi Lin},
ZBLNUMBER = {1116.53055},
} -
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AUTHOR = {Aldi, Marco and Zaslow, Eric},
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YEAR = {2005},
NUMBER = {6},
PAGES = {019, 14 pp.},
ISSN = {1126-6708},
MRCLASS = {81T30 (14J81 32J81 81T75)},
MRNUMBER = {2158557},
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DOI = {10.1088/1126-6708/2005/06/019},
} -
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AUTHOR = {Alekseev, A. and Bursztyn, H. and Meinrenken, E.},
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FJOURNAL = {Astérisque},
NUMBER = {327},
YEAR = {2009},
PAGES = {131--199 (2010)},
ISSN = {0303-1179},
ISBN = {978-2-85629-288-4},
MRCLASS = {53D18 (53Cxx)},
MRNUMBER = {2642360},
ZBLNUMBER = {05765012},
} -
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@misc{Gu,
author={Gualtieri, Marco},
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YEAR={2004},
ARXIV={math.DG/0401221},
} -
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} -
@misc{Sevlet,
author={{Š}evera, P.},
TITLE={Letters to {A}. {W}einstein concerning {C}ourant algebroids, 1998--2000},
URL={http://sophia.dtp.fmph.uniba.sk/~severa/letters/},
} -
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TITLE = {Poisson geometry with a 3-form background},
JOURNAL = {Progr. Theoret. Phys. Suppl.},
FJOURNAL = {Progress of Theoretical Physics. Supplement},
NUMBER = {144},
YEAR = {2001},
PAGES = {145--154},
ISSN = {0375-9687},
MRCLASS = {53D17},
MRNUMBER = {2023853},
MRREVIEWER = {Kyousuke Uchino},
ZBLNUMBER = {1029.53090},
DOI = {doi:10.1143/PTPS.144.145},
} -
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@article {WeinPo, MRKEY = {0723816},
AUTHOR = {Weinstein, Alan},
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JOURNAL = {J. Differential Geom.},
FJOURNAL = {Journal of Differential Geometry},
VOLUME = {18},
YEAR = {1983},
NUMBER = {3},
PAGES = {523--557},
ISSN = {0022-040X},
CODEN = {JDGEAS},
MRCLASS = {58F05 (22E60 53C15 53C57)},
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ZBLNUMBER = {0524.58011},
} -
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@article {Weinmod, MRKEY = {1484598},
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DOI = {10.1016/S0393-0440(97)80011-3},
ZBLNUMBER = {0902.58013},
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@book {Wells, MRKEY = {0608414},
AUTHOR = {Wells, Jr., R. O.},
TITLE = {Differential Analysis on Complex Manifolds},
SERIES = {Grad. Texts in Math.},
VOLUME = {65},
EDITION = {Second},
PUBLISHER = {Springer-Verlag},
ADDRESS = {New York},
YEAR = {1980},
PAGES = {x+260},
ISBN = {0-387-90419-0},
MRCLASS = {58-01 (32-01)},
MRNUMBER = {0608414},
MRREVIEWER = {Daniel M. Burns, Jr.},
ZBLNUMBER = {0435.32004},
} -
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@article {zambon, MRKEY = {2471097},
AUTHOR = {Zambon, Marco},
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MRCLASS = {53D18 (53D17)},
MRNUMBER = {2471097},
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ZBLNUMBER = {1172.53050},
}