Speaker
Leonardo Roa-Leguizamón
(Universidade Estadual de Campinas, Brazil)
Description
Let $X$ be a smooth, irreducible, projective surface. A coherent system on $X$ is a pair $(E, V)$ where $E$ is a coherent sheaf on $X$ and $V$ is a finite-dimensional vector space. Associated to coherent systems there is a notion of stability that depends on a parameter $\alpha \in \mathbb{Q}[m]$. In this talk, we describe the moduli space of coherent systems for $\alpha \gg 0$, present topological and geometric properties of this moduli space, and describe the structure of chambers and walls for coherent systems on the projective plane when $\dim(V) = 2$.
This is joint work with L. Costa, I. Macías-Tarrío, and a joint work with O. Mata-Gutiérrez, and H. Torres-López.
