Exceptional pairs on del Pezzo surfaces and spaces of compatible Feigin-Odesskii brackets
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912835579150336 |
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| author | Polishchuk, Alexander Rains, Eric |
| author_facet | Polishchuk, Alexander Rains, Eric |
| contents | We prove that for every relatively prime pair of integers $(d,r)$ with $r>0$, there exists an exceptional pair $({\mathcal O},V)$ on any del Pezzo surface of degree 4, such that $V$ is a bundle of rank $r$ and degree $d$. As an application, we prove that every Feigin-Odesskii Poisson bracket on a projective space can be included into a 5-dimensional linear space of compatible Poisson brackets. We also construct new examples of linear spaces of compatible Feigin-Odesskii Poisson brackets of dimension $>5$, coming from del Pezzo surfaces of degree $>4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_19307 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exceptional pairs on del Pezzo surfaces and spaces of compatible Feigin-Odesskii brackets Polishchuk, Alexander Rains, Eric Algebraic Geometry We prove that for every relatively prime pair of integers $(d,r)$ with $r>0$, there exists an exceptional pair $({\mathcal O},V)$ on any del Pezzo surface of degree 4, such that $V$ is a bundle of rank $r$ and degree $d$. As an application, we prove that every Feigin-Odesskii Poisson bracket on a projective space can be included into a 5-dimensional linear space of compatible Poisson brackets. We also construct new examples of linear spaces of compatible Feigin-Odesskii Poisson brackets of dimension $>5$, coming from del Pezzo surfaces of degree $>4$. |
| title | Exceptional pairs on del Pezzo surfaces and spaces of compatible Feigin-Odesskii brackets |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2407.19307 |