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arXiv · 1905.00246

On degeneracy loci of equivariant bi-vector fields on a smooth toric variety

Elena Martinengo
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Abstract

We study equivariant bi-vector fields on a toric variety. We prove that, on a smooth toric variety of dimension $n$, the locus where the rank of an equivariant bi-vector field is $\leq 2k$ is not empty and has at least a component of dimension $\geq 2k+1$, for all integers $k> 0$ such that $2k < n$. The same is true also for $k=0$, if the toric variety is smooth and compact. While for the non compact case, the locus in question has to be assumed to be non empty.

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Elena Martinengo. 2019-05-01. On degeneracy loci of equivariant bi-vector fields on a smooth toric variety. https://arxiv.org/abs/1905.00246

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