Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



Singularités symplectiques

Author: Stéphane Druel
Journal: J. Algebraic Geom. 13 (2004), 427-439
Published electronically: December 8, 2003
MathSciNet review: 2047675
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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 $\frac {1}{3}(1,2,\ldots ,1,2)$.

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    [Ar68]Ar68M. Artin, On the solutions of analytic equations, Invent. Math. 5 (1968), 277-291. [Be00]Be00A. Beauville, Symplectic singularities, Invent. Math. 139 (2000), 541-549. [CF01]CF01F. Campana, H. Flenner, Contact singularities à paraître dans Manuscripta Math. 108 (2002), 529–541. [De01]De01O. Debarre, Higher-dimensional algebraic geometry, Universitext, Springer-Verlag, 2001. [Fl88]Fl88H. Flenner, Extendability of differential forms on non-isolated singularities, Invent. Math. 94 (1988), 317-326. [Fu87]Fu87T. Fujita, On polarized manifolds whose adjoint bundles are not semipositive, Algebraic geometry, Sendai 1985, Adv. Stud. Pure Math. 10, 167-178, 1987. [Gr66]Gr66A. Grothendieck, Eléments de géométrie algébrique III, Inst. Hautes Etudes Sci. Publ. Math. 11, 1966. [Gr71]Gr71A. Grothendieck, Revêtements étales et groupe fondamental, Lecture Notes in Math. 224, Springer-Verlag, 1971. [KO73]KO73S. Kobayashi, T. Ochiai, Characterization of complex projective spaces and hyperquadrics, J. Math. Kyoto Univ. 13 (1973), 31-47. [Mo82]Mo82S. Mori, Threefolds whose canonical bundles are not numerically effective, Ann. of Math. 116 (1982), 133-176. [Od88]Od88T. Oda, Convex Bodies and Algebraic Geometry 15, Springer-Verlag, 1988. [Wi89]Wi89J. Wisniewski, Length of extremal rays and generalized adjonction, Math. Z. 200 (1989), 409-427. [Wi90]Wi90J. Wisniewski, On a conjecture of Mukai, Manuscripta Math. 68 (1990), 135-141. [Wi91]Wi91J. 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
MR Author ID: 639659

Received by editor(s): January 4, 2002
Published electronically: December 8, 2003