Singularités symplectiques
Author:
Stéphane Druel
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
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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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[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.
[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
Email:
druel@mozart.ujf-grenoble.fr
Received by editor(s):
January 4, 2002
Published electronically:
December 8, 2003
