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arXiv · 2407.19307

Exceptional pairs on del Pezzo surfaces and spaces of compatible Feigin-Odesskii brackets

Alexander Polishchuk·Eric Rains
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Abstract

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 $>4$.

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Alexander Polishchuk, Eric Rains. 2024-07-27. Exceptional pairs on del Pezzo surfaces and spaces of compatible Feigin-Odesskii brackets. https://doi.org/10.1017/s1474748025101333

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