no. 2
A survey on symplectic singularities and symplectic resolutions
Fu, Baohua1
1 Laboratoire J. Leray Université de Nantes, Faculté des sciences 2, Rue de la Houssinière BP 92208, F-44322 Nantes Cedex 03 France
Annales mathématiques Blaise Pascal, Tome 13 (2006) no. 2, pp. 209-236.

This is a survey written in an expositional style on the topic of symplectic singularities and symplectic resolutions.

DOI : 10.5802/ambp.218
Fu, Baohua 1

1 Laboratoire J. Leray Université de Nantes, Faculté des sciences 2, Rue de la Houssinière BP 92208, F-44322 Nantes Cedex 03 France 
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Fu, Baohua. A survey on symplectic singularities and symplectic resolutions. Annales mathématiques Blaise Pascal, Tome 13 (2006) no. 2, pp. 209-236. doi : 10.5802/ambp.218. http://www.numdam.org/articles/10.5802/ambp.218/

[1] Batyrev, V. Stringy Hodge numbers of varieties with Gorenstein canonical singularities, Integrable systems and algebraic geometry (Kobe/Kyoto, 1997), Publish or Perish, Inc., Houston, 1998, pp. 1-32 | MR

[2] Batyrev, V. Non-Archimedean integrals and stringy Euler numbers of log-terminal pairs, J. Eur. Math. Soc., Volume 1 (1999), pp. 5-33 | DOI | MR | Zbl

[3] Beauville, A. Fano contact manifolds and nilpotent orbits, Comment. Math. Helv, Volume 73 (1998), pp. 566-583 | DOI | MR | Zbl

[4] Beauville, A. Symplectic singularities, Invent. Math., Volume 139 (2000), pp. 541-549 | DOI | MR | Zbl

[5] Bezrukavnikov, R.; Kaledin, D. McKay equivalence for symplectic resolutions of singularities, Proc. Steklov Inst. Math., Volume 246 (2004), pp. 13-33 | MR | Zbl

[6] Bialynicki-Birula, A. Some theorems on actions of algebraic groups, Ann. of Math. (2), Volume 98 (1973), pp. 480-497 | DOI | MR | Zbl

[7] Bottacin, F. Poisson structures on moduli spaces of sheaves over Poisson surfaces, Invent. Math., Volume 121 (1995), pp. 421-436 | DOI | MR | Zbl

[8] Burns, D.; Hu, Y.; Luo, T. HyperKähler manifolds and birational transformations in dimension 4, Vector bundles and representation theory (Columbia, MO, 2002), Amer. Math. Soc., 2003, pp. 141-149 | MR | Zbl

[9] Cho, Y.; Miyaoka, Y.; Shepherd-Barron, N.; Miyaoka; Mori Characterizations of projective space and applications to complex symplectic manifolds, Higher dimensional birational geometry (Kyoto, 1997), Math. Soc. Japan, 2002, pp. 1-88 | MR | Zbl

[10] Choy, J.; Kiem, Y.-H. Nonexistence of crepant resolution of some moduli spaces of sheaves on a K3 surface (2004) (math.AG/0407100)

[11] Choy, J.; Kiem, Y.-H. On the existence of a crepant resolution of some moduli spaces of sheaves on an abelian surface, Math. Z., Volume 252 (2006), pp. 557-575 | DOI | MR

[12] Cohen, A. M. Finite quaternionic reflection groups, J. Algebra, Volume 64 (1980), pp. 293-324 | DOI | MR | Zbl

[13] Collingwood, D.; Mc Govern, W. Nilpotent orbits in semi-simple Lie algebras, Van Nostrand Reinhold Co., New York, 1993 | MR | Zbl

[14] Druel, S. Singularités symplectiques, J. Algebraic Geom., Volume 13 (2004), pp. 427-439 | MR | Zbl

[15] Fu, B. Symplectic resolutions for coverings of nilpotent orbits, C. R. Acad. Sci., Volume 336 (2003), pp. 159-162 | MR | Zbl

[16] Fu, B. Symplectic resolutions for nilpotent orbits, Invent. Math., Volume 151 (2003), pp. 167-186 | DOI | MR | Zbl

[17] Fu, B. Symplectic resolutions for nilpotent orbits (II), C. R. Acad. Sci., Volume 337 (2003), pp. 277-281 | MR | Zbl

[18] Fu, B. Birational geometry in codimension 2 of symplectic resolutions (2004) (math.AG/0409224)

[19] Fu, B. Extremal contractions, stratified Mukai flops and Springer maps (2006) (math.AG/0605431)

[20] Fu, B. Mukai flops and deformations of symplectic resolutions, Math. Z., Volume 253 (2006), pp. 87-96 | DOI | MR | Zbl

[21] Fu, B.; Namikawa, Y. Uniqueness of crepant resolutions and symplectic singularities, Ann. Inst. Fourier, Volume 54 (2004), pp. 1-19 | DOI | Numdam | MR | Zbl

[22] Ginzburg, V.; Kaledin, D. Poisson deformations of symplectic quotient singularities, Adv. Math., Volume 186 (2004), pp. 1-57 | DOI | MR | Zbl

[23] Gordon, I. Baby Verma modules for rational Cherednik algebras, Bull. London Math. Soc., Volume 35 (2003), pp. 321-336 | DOI | MR | Zbl

[24] Guralnick, Robert M.; Saxl, J. Generation of finite almost simple groups by conjugates, J. Algebra, Volume 268 (2003), pp. 519-571 | DOI | MR | Zbl

[25] Hartshorne, R. Algebraic Geometry, Springer-Verlag, 1977 | MR | Zbl

[26] Hesselink, W. Polarizations in the classical groups, Math. Z., Volume 160 (1978), pp. 217-234 | DOI | MR | Zbl

[27] Hu, Y. Geometric Invariant Theory and Birational Geometry (2005) (math.AG/0502462)

[28] Hu, Y.; Yau, S.-T. HyperKähler manifolds and birational transformations, Adv. Theor. Math. Phys., Volume 6 (2002), pp. 557-574 | MR | Zbl

[29] Huybrechts, D. Compact hyper-Kähler manifolds: basic results, Invent. Math., Volume 135 (1999), pp. 63-113 | DOI | MR | Zbl

[30] Kaledin, D. Symplectic singularities from the Poisson point of view, J. Reine Angew. Math.

[31] Kaledin, D. Symplectic resolutions: deformations and birational maps (2000) (math.AG/0012008)

[32] Kaledin, D. McKay correspondence for symplectic quotient singularities, Invent. math., Volume 148 (2002), pp. 150-175 | DOI | MR | Zbl

[33] Kaledin, D. On crepant resolutions of symplectic quotient singularities, Selecta Math. (N.S.), Volume 9 (2003), pp. 529-555 | DOI | MR | Zbl

[34] Kaledin, D. Derived equivalence by quantization (2005) (math.AG/0504584)

[35] Kaledin, D.; Lehn, M. Local structure of hyperKaehler singularities in O’Grady’s examples (2004) (math.AG/0405575)

[36] Kaledin, D.; Lehn, M.; Sorger, C. Singular symplectic moduli spaces, Invent. Math., Volume 164 (2006), pp. 591-614 | DOI | MR | Zbl

[37] Kawamata, Y. D-equivalence and K-equivalence, J. Differential Geom., Volume 61 (2002), pp. 147-171 | MR | Zbl

[38] Kraft, H.; Procesi, C. Closures of conjugacy classes of matrices are normal, Invent. Math., Volume 53 (1979), pp. 227-247 | DOI | MR | Zbl

[39] Markman, E. Brill-Noether duality for moduli spaces of sheaves of K3 surfaces, J. Algebr. Geom., Volume 10 (2001), pp. 623-694 | MR | Zbl

[40] Mukai, S. Symplectic structure of the moduli space of sheaves on an abelian or K3 surface, Invent. Math., Volume 77 (1984), pp. 101-116 | DOI | MR | Zbl

[41] Namikawa, Y. Deformation theory of singular symplectic n-folds, Math. Ann., Volume 319 (2001), pp. 597-623 | DOI | MR | Zbl

[42] Namikawa, Y. Extension of 2-forms and symplectic varieties, J. Reine Angew. Math., Volume 539 (2001), pp. 123-147 | DOI | MR | Zbl

[43] Namikawa, Y. A note on symplectic singularitie (2001) (math.AG/0101028)

[44] Namikawa, Y. Birational geometry of symplectic resolutions of nilpotent orbits (2004) (math.AG/0404072)

[45] Namikawa, Y. Birational geometry of symplectic resolutions of nilpotent orbits II (2004) (math.AG/0408274)

[46] Namikawa, Y. Flops and Poisson deformations of symplectic varieties (2005) (math.AG/0510059)

[47] Namikawa, Y. On deformations of Q-factorial symplectic varieties (2005) (math.AG/0506534)

[48] O’Grady, K. Desingularized moduli spaces of sheaves on a K3, J. reine angew. Math., Volume 512 (1999), pp. 49-117 | DOI | MR | Zbl

[49] O’Grady, K. A new six-dimensional irreducible symplectic variety, J. Algebraic Geom., Volume 12 (2003), pp. 435-505 | DOI | MR | Zbl

[50] Panyushev, D. Rationality of singularities and the Gorenstein property for nilpotent orbits, Funct. Anal. Appl., Volume 25 (1991), pp. 225-226 | DOI | MR | Zbl

[51] Verbitsky, M. Holomorphic symplectic geometry and orbifold singularities, Asian J. Math., Volume 4 (2000), pp. 553-563 | MR | Zbl

[52] Wierzba, J. Contractions of symplectic varieties, J. Algebraic Geom., Volume 12 (2003), pp. 507-534 | DOI

[53] Wierzba, J.; Wisniewski, J. A. Small contractions of symplectic 4-folds, Duke Math. J., Volume 120 (2003), pp. 65-95 | DOI

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