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Elliptic singularities on log symplectic manifolds and Feigin–Odesskii Poisson brackets
| Content Provider | Scilit |
|---|---|
| Author | Pym, Brent |
| Copyright Year | 2017 |
| Description | Journal: Compositio Mathematica A log symplectic manifold is a complex manifold equipped with a complex symplectic form that has simple poles on a hypersurface. The possible singularities of such a hypersurface are heavily constrained. We introduce the notion of an elliptic point of a log symplectic structure, which is a singular point at which a natural transversality condition involving the modular vector field is satisfied, and we prove a local normal form for such points that involves the simple elliptic surface singularities $\widetilde{E}_{6},\widetilde{E}_{7}$ and $\widetilde{E}_{8}$. Our main application is to the classification of Poisson brackets on Fano fourfolds. For example, we show that Feigin and Odesskii’s Poisson structures of type $q_{5,1}$ are the only log symplectic structures on projective four-space whose singular points are all elliptic. |
| Ending Page | 744 |
| Starting Page | 717 |
| ISSN | 00221295 |
| e-ISSN | 15705846 |
| DOI | 10.1112/s0010437x16008174 |
| Journal | Compositio Mathematica |
| Issue Number | 4 |
| Volume Number | 153 |
| Language | English |
| Publisher | Wiley-Blackwell |
| Publisher Date | 2017-03-13 |
| Access Restriction | Open |
| Subject Keyword | Journal: Compositio Mathematica Mathematical Physics |
| Content Type | Text |
| Resource Type | Article |
| Subject | Algebra and Number Theory |
