Contractions of Symplectic Varieties
| dc.creator | Wierzba, Jan | |
| dc.date | 1999-10-25 | |
| dc.date | 2000-06-12 | |
| dc.date.accessioned | 2026-07-07T05:31:16Z | |
| dc.date.available | 2026-07-07T05:31:16Z | |
| dc.description | We consider birational projective contractions f:X -> Y from a smooth symplectic variety X over the complex numbers. We first show that exceptional rational curves on X deform in a family of dimension at least 2n-2. Then we show that these contractions are generically coisotropic, provided X is projective. Then we specialize to contractions with 1-dimensional exceptional fibres. We classify them in a natural way in terms of (Γ, G), where Γis a Dynkin diagram of type A_l, D_l or E_l and G is a permutation group of automorphisms of Γ. The 1-dimensional fibres do not degenerate, except if the contraction is of type (A_{2l},S_2). In that case they do not degenerate in codimension 1. Furthermore we show that the normalization of any irreducible component of Sing(Y) is a symplectic variety. We also provide examples for contractions of any type (Γ, G). | |
| dc.description | LaTeX, 26 pages with 7 figures. Section 2 contains new results | |
| dc.identifier | https://arxiv.org/abs/math/9910130 | |
| dc.identifier | http://arxiv.org/abs/math/9910130 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/79279 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14E15; 14B07 | |
| dc.title | Contractions of Symplectic Varieties | |
| dc.type | text |