Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 

 

Singularités symplectiques


Author: Stéphane Druel
Translated by:
Journal: J. Algebraic Geom. 13 (2004), 427-439
DOI: https://doi.org/10.1090/S1056-3911-03-00356-4
Published electronically: December 8, 2003
MathSciNet review: 2047675
Full-text PDF

Abstract | References | Additional Information

Abstract: We classify isolated symplectic singularities of dimension greater or equal to 6 such that the normalized blow-up of the singular point is a resolution of singularities whose exceptional locus is a reduced simple normal crossing divisor with at least two irreducible components. They are isomorphic to the quotient singularities of type $\frac{1}{3}(1,2,\ldots,1,2)$.


References [Enhancements On Off] (What's this?)

  • [Ar68] M. Artin, On the solutions of analytic equations, Invent. Math. 5 (1968), 277-291.
  • [Be00] A. Beauville, Symplectic singularities, Invent. Math. 139 (2000), 541-549.
  • [CF01] F. Campana, H. Flenner, Contact singularities à paraître dans Manuscripta Math. 108 (2002), 529-541.
  • [De01] O. Debarre, Higher-dimensional algebraic geometry, Universitext, Springer-Verlag, 2001.
  • [Fl88] H. Flenner, Extendability of differential forms on non-isolated singularities, Invent. Math. 94 (1988), 317-326.
  • [Fu87] T. Fujita, On polarized manifolds whose adjoint bundles are not semipositive, Algebraic geometry, Sendai 1985, Adv. Stud. Pure Math. 10, 167-178, 1987.
  • [Gr66] A. Grothendieck, Eléments de géométrie algébrique III, Inst. Hautes Etudes Sci. Publ. Math. 11, 1966.
  • [Gr71] A. Grothendieck, Revêtements étales et groupe fondamental, Lecture Notes in Math. 224, Springer-Verlag, 1971.
  • [KO73] S. Kobayashi, T. Ochiai, Characterization of complex projective spaces and hyperquadrics, J. Math. Kyoto Univ. 13 (1973), 31-47.
  • [Mo82] S. Mori, Threefolds whose canonical bundles are not numerically effective, Ann. of Math. 116 (1982), 133-176.
  • [Od88] T. Oda, Convex Bodies and Algebraic Geometry 15, Springer-Verlag, 1988.
  • [Wi89] J. Wisniewski, Length of extremal rays and generalized adjonction, Math. Z. 200 (1989), 409-427.
  • [Wi90] J. Wisniewski, On a conjecture of Mukai, Manuscripta Math. 68 (1990), 135-141.
  • [Wi91] J. Wisniewski, On contractions of extremal rays on Fano manifolds, J. Reine Angew. Math. 417 (1991), 141-157.


Additional Information

Stéphane Druel
Affiliation: Institut Fourier, UMR 5582 du CNRS, Université Joseph Fourier, BP 74, 38402 Saint Martin d’Hères, France
Email: druel@mozart.ujf-grenoble.fr

DOI: https://doi.org/10.1090/S1056-3911-03-00356-4
Received by editor(s): January 4, 2002
Published electronically: December 8, 2003

Journal of Algebraic Geometry
The Journal of Algebraic Geometry
is sponsored by the Department of Mathematical Sciences
of Tsinghua University
and is distributed by the American Mathematical Society
for University Press, Inc.
Online ISSN 1534-7486; Print ISSN 1056-3911
© 2017 University Press, Inc.
Comments: jag-query@ams.org
AMS Website