Year: 2025
Type: article
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 $>4$ .
Authors: Alexander Polishchuk, Eric Rains
Institutions: University of Oregon, California Institute of Technology
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4414928706