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A finiteness theorem on symplectic singularities.
- Source :
-
Compositio Mathematica . Jun2016, Vol. 152 Issue 6, p1225-1236. 12p. - Publication Year :
- 2016
-
Abstract
- An affine symplectic singularity $X$ with a good $\mathbf{C}^{\ast }$-action is called a conical symplectic variety. In this paper we prove the following theorem. For fixed positive integers $N$ and $d$, there are only a finite number of conical symplectic varieties of dimension $2d$ with maximal weights $N$, up to an isomorphism. To prove the main theorem, we first relate a conical symplectic variety with a log Fano Kawamata log terminal (klt) pair, which has a contact structure. By the boundedness result for log Fano klt pairs with fixed Cartier index, we prove that conical symplectic varieties of a fixed dimension and with a fixed maximal weight form a bounded family. Next we prove the rigidity of conical symplectic varieties by using Poisson deformations. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0010437X
- Volume :
- 152
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- Compositio Mathematica
- Publication Type :
- Academic Journal
- Accession number :
- 116638150
- Full Text :
- https://doi.org/10.1112/S0010437X16007387