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A finiteness theorem on symplectic singularities
| Content Provider | Scilit |
|---|---|
| Author | Namikawa, Yoshinori |
| Copyright Year | 2016 |
| Description | Journal: Compositio Mathematica 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. |
| Ending Page | 1236 |
| Starting Page | 1225 |
| ISSN | 00221295 |
| e-ISSN | 15705846 |
| DOI | 10.1112/s0010437x16007387 |
| Journal | Compositio Mathematica |
| Issue Number | 6 |
| Volume Number | 152 |
| Language | English |
| Publisher | Wiley-Blackwell |
| Publisher Date | 2016-04-15 |
| Access Restriction | Open |
| Subject Keyword | Journal: Compositio Mathematica Symplectic Varieties Conical Symplectic Affine Symplectic Singularity Log Fano |
| Content Type | Text |
| Resource Type | Article |
| Subject | Algebra and Number Theory |
