Geometry and topology of symplectic resolutions

This is an overview of math.AG/0310186, math.AG/0309290, math.AG/0501247, math.AG/0401002 and math.AG/0504584 written for the Proceedings of the AMS Meeting on Algebraic Geometry, Seattle, 2005.

[1]  T. Bridgeland Derived categories of coherent sheaves , 2006, math/0602129.

[2]  D. Rumynin,et al.  Singular Localization and Intertwining Functors for Reductive Lie Algebras in Prime Characteristic , 2006, Nagoya Mathematical Journal.

[3]  D. Kaledin Derived Equivalences by Quantization , 2005, math/0504584.

[4]  M. Lehn,et al.  Singular symplectic moduli spaces , 2005, math/0504202.

[5]  R. Bezrukavnikov,et al.  Fedosov quantization in positive characteristic , 2005, math/0501247.

[6]  V. Drinfeld QUANTIZATION OF HITCHIN’S INTEGRABLE SYSTEM AND HECKE EIGENSHEAVES , 2005 .

[7]  Kobi Kremnizer,et al.  Localization for quantum groups at a root of unity , 2004, math/0407048.

[8]  M. Lehn,et al.  Local structure of hyperkaehler singularities in O'Grady's examples , 2004, math/0405575.

[9]  H. Esnault,et al.  Lectures on Vanishing Theorems , 2004 .

[10]  I. Gordon,et al.  Representations of symplectic reflection algebras and resolutions of deformations of symplectic quotient singularities , 2003, math/0310187.

[11]  D. Kaledin,et al.  Fedosov quantization in algebraic context , 2003, math/0309290.

[12]  Baohua Fu,et al.  Uniqueness of crepant resolutions and symplectic singularities , 2003, math/0306091.

[13]  Y. Namikawa Mukai flops and derived categories II , 2003, math/0305086.

[14]  Baohua Fu Symplectic resolutions for nilpotent orbits , 2002, math/0205048.

[15]  V. Ginzburg,et al.  Poisson deformations of symplectic quotient singularities , 2002, math/0212279.

[16]  M. Bergh Three-dimensional flops and noncommutative rings , 2002, math/0207170.

[17]  D. Rumynin,et al.  Localization of modules for a semisimple Lie algebra in prime characteristic (with an Appendix by R. Bezrukavnikov and S. Riche: Computation for sl(3)) , 2002, math/0205144.

[18]  Y. Kawamata D-Equivalence and K-Equivalence , 2002, math/0205287.

[19]  Y. Namikawa Mukai flops and derived categories , 2002, math/0203287.

[20]  V. Ginzburg,et al.  Symplectic reflection algebras, Calogero-Moser space, and deformed Harish-Chandra homomorphism , 2000, math/0011114.

[21]  Y. Namikawa Deformation theory of singular symplectic n-folds , 2000, math/0010113.

[22]  Y. Namikawa Extension of 2-forms and symplectic varieties , 2000, math/0010114.

[23]  T. Bridgeland Flops and derived categories , 2000, math/0009053.

[24]  M. Verbitsky,et al.  Period Map for Non-Compact Holomorphically Symplectic Manifolds , 2000, math/0005007.

[25]  A. Beauville Symplectic singularities , 1999, math/9903070.

[26]  Miles Reid,et al.  Mukai implies McKay: the McKay correspondence as an equivalence of derived categories , 1999, math/9908027.

[27]  M. Verbitsky Holomorphic symplectic geometry and orbifold singularities , 1999, math/9903175.

[28]  N. Chriss,et al.  Representation theory and complex geometry , 1997 .

[29]  P. Etingof,et al.  Quantization of Lie bialgebras, I , 1995, q-alg/9506005.

[30]  A.Bondal,et al.  Semiorthogonal decomposition for algebraic varieties , 1995, alg-geom/9506012.

[31]  A. Bondal,et al.  Semiorthogonal decompositions for algebraic varieties. , 1995 .

[32]  R. Carter,et al.  INTRODUCTION TO QUANTUM GROUPS (Progress in Mathematics 110) , 1995 .

[33]  N. Reshetikhin,et al.  Quantum Groups , 1993, hep-th/9311069.

[34]  H. Nakajima Instantons on ALE spaces, quiver varieties, and Kac-Moody algebras , 1994 .

[35]  B. Fedosov A simple geometrical construction of deformation quantization , 1994 .

[36]  A. Beilinson,et al.  A proof of Jantzen conjectures , 1993 .

[37]  George Lusztig,et al.  Introduction to Quantum Groups , 1993 .

[38]  Nicolai Reshetikhin,et al.  Quantum Groups , 1993 .

[39]  Y. Kawamata Unobstructed deformations-a remark on a paper of Z. Ran, Correction , 1992 .

[40]  C. Procesi,et al.  Homology of the zero-set of a nilpotent vector field on a flag manifold , 1988 .

[41]  D. Gorenstein,et al.  Algebraic approximation of structures over complete local rings , 1969 .