A construction of equivariant bundles on the space of symmetric forms

Ada Boralevi; Daniele Faenzi; Paolo Lella

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arXiv · 1804.06211

A construction of equivariant bundles on the space of symmetric forms

Ada Boralevi·Daniele Faenzi·Paolo Lella

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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.

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Ada Boralevi, Daniele Faenzi, Paolo Lella. 2018-04-17. A construction of equivariant bundles on the space of symmetric forms. https://arxiv.org/abs/1804.06211

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