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

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 ≤ 2k is not empty and has at least a component of dimension ≥ 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.

Rend. Mat. Appl. (7) 40 (2019) 81-95; pdf