JournalsrmiVol. 38, No. 3pp. 761–782

A construction of equivariant bundles on the space of symmetric forms

  • Ada Boralevi

    Politecnico di Torino, Italy
  • Daniele Faenzi

    Université de Bourgogne et Franche Comté, Dijon, France
  • Paolo Lella

    Politecnico di Milano, Italy
A construction of equivariant bundles on the space of symmetric forms cover
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Abstract

We construct stable vector bundles on the space P(SdCn+1)\mathbb{P}(S^d \mathbb{C}^{n+1}) of symmetric forms of degree dd in n+1n+1 variables which are equivariant for the action of SLn+1(C)\text{SL}_{n+1}(\mathbb{C}) and admit an equivariant free resolution of length 22. For n=1n=1, we obtain new examples of stable vector bundles of rank d1d-1 on Pd\mathbb{P}^d, which are moreover equivariant for SL2(C)\operatorname{SL}_2(\mathbb{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.

Cite this article

Ada Boralevi, Daniele Faenzi, Paolo Lella, A construction of equivariant bundles on the space of symmetric forms. Rev. Mat. Iberoam. 38 (2022), no. 3, pp. 761–782

DOI 10.4171/RMI/1307