Contractions of Symplectic Varieties

dc.creatorWierzba, Jan
dc.date1999-10-25
dc.date2000-06-12
dc.date.accessioned2026-07-07T05:31:16Z
dc.date.available2026-07-07T05:31:16Z
dc.descriptionWe 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.descriptionLaTeX, 26 pages with 7 figures. Section 2 contains new results
dc.identifierhttps://arxiv.org/abs/math/9910130
dc.identifierhttp://arxiv.org/abs/math/9910130
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/79279
dc.subjectAlgebraic Geometry
dc.subject14E15; 14B07
dc.titleContractions of Symplectic Varieties
dc.typetext

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