Mathematics – Algebraic Geometry
Scientific paper
2012-03-20
Mathematics
Algebraic Geometry
33 pages
Scientific paper
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.
Gualtieri Marco
Pym Brent
No associations
LandOfFree
Poisson modules and degeneracy loci does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Poisson modules and degeneracy loci, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Poisson modules and degeneracy loci will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-493469