Moduli of generalized syzygy bundles

by Barbara Fantechi (Trieste)

Wednesday 13 Mar 2024, 16:00 → 17:00 Europe/Rome

Aula Seminari (Department of Mathematics)

Given a vector bundle $F$ on a variety $X$ of dimension at least 2 and $W\subset H^0(F)$ such that the evaluation map $W\otimes O_X\to F$ is surjective, its kernel is called a generalized syzygy bundle.

Under mild assumptions, we construct a moduli space of simple generalized syzygy bundles, and show that the natural morphism to the moduli of simple sheaves is a locally closed embedding. If moreover  $H^1(X,O_X)=0$ and dim X>2, we find an explicit open subspace in the moduli space of simple generalized syzygy bundles where the restriction of the natural morphism to the moduli of simple sheaves is an open embedding.