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

Luogo: l'evento si terrà per via telematica attraverso collegamento alla piattaforma Zoom. Per partecipare richiedere le credenziali alla segreteria - dept.math [at] unitn.it

Ore: 14.00

Relatrice:

• Elena Martinengo (Università degli Studi di Torino)

Abstract

On a smooth toric variety X of dimension n, we study equivariant bi-vector fields, i.e. global sections of the
second symmetric power of the homolorphic tangent bundle that are equivariant with respect to the toric action.
We are interested in the degeneracy loci, that are the loci in which the rank of such a bi-vector field is less or
equal some integer k. In particular, in the spirit of a Bondal conjecture, we prove that 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.

Referenti: Luis E. Solá Conde, Elisa Postinghel, Camilla Felisetti