A construction of equivariant bundles on the space of symmetric forms
Algebraic Geometry
2018-04-18 v1 Representation Theory
Abstract
We construct stable vector bundles on the space of symmetric forms of degree d in n+1 variables which are equivariant for the action of SL_{n+1}(C), and admit an equivariant free resolution of length 2. For n=1, we obtain new examples of stable vector bundles of rank d-1 on P^d, which are moreover equivariant for SL_2(C). The presentation matrix of these bundles attains Westwick's upper bound for the dimension of vector spaces of matrices of constant rank and fixed size.
Keywords
Cite
@article{arxiv.1804.06211,
title = {A construction of equivariant bundles on the space of symmetric forms},
author = {Ada Boralevi and Daniele Faenzi and Paolo Lella},
journal= {arXiv preprint arXiv:1804.06211},
year = {2018}
}
Comments
Ancillary file containing M2 package available at http://www.paololella.it/EN/Publications_files/SLnEquivariantMatrices.m2