Poisson modules and degeneracy loci
| Autor: | Marco Gualtieri, Brent Pym |
|---|---|
| Rok vydání: | 2012 |
| Předmět: |
Mathematics - Differential Geometry
Pure mathematics General Mathematics Holomorphic function Fano plane Poisson distribution 01 natural sciences 53D17 14C17 32S65 Volume form Mathematics - Algebraic Geometry symbols.namesake Mathematics::Algebraic Geometry Line bundle Poisson manifold 0103 physical sciences FOS: Mathematics 0101 mathematics Mathematics::Symplectic Geometry Algebraic Geometry (math.AG) Meromorphic function Mathematics Conjecture 010102 general mathematics Differential Geometry (math.DG) Mathematics - Symplectic Geometry symbols Symplectic Geometry (math.SG) 010307 mathematical physics |
| DOI: | 10.48550/arxiv.1203.4293 |
| Popis: | In this paper, we study the interplay between modules and sub-objects in holomorphic Poisson geometry. In particular, we define a new notion of "residue" for a Poisson module, analogous to the Poincar\'e residue of a meromorphic volume form. Of particular interest is the interaction between the residues of the canonical line bundle of a Poisson manifold and its degeneracy loci---where the rank of the Poisson structure drops. As an application, we provide new evidence in favour of Bondal's conjecture that the rank \leq 2k locus of a Fano Poisson manifold always has dimension \geq 2k+1. In particular, we show that the conjecture holds for Fano fourfolds. We also apply our techniques to a family of Poisson structures defined by Fe\u{\i}gin and Odesski\u{\i}, where the degeneracy loci are given by the secant varieties of elliptic normal curves. Comment: 33 pages |
| Databáze: | OpenAIRE |
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