A construction of equivariant bundles on the space of symmetric forms

Abstract

We construct stable vector bundles on the space P(S d C n+1 ) of symmetric forms of degree d in n + 1 variables which are equivariant for the action of SLn+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 SL2(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.