Tim Ryan : An introduction to moduli spaces of sheaves on $\mathbb{P}^1 \times \mathbb{P}^1$

Posted by Tim Ryan , part of the Graduate Algebraic Geometry Seminar.

At

Sept. 30, 2015, 3 p.m.

In

SEO 712

Abstract

We will introduce moduli spaces of sheaves starting with the history of their construction. We will then specialize to the case of moduli spaces of sheaves on $\mathbb{P}^1 \times \mathbb{P}^1$. In this setting, we will discuss properties of the moduli spaces including nonemptiness. Furthermore, we will consider results showing they are $\mathbb{Q}$-factorial and Mori dream spaces. Being MDS's, we are interested in their effective cones so we then will give the general strategy for computing effective cones. We will apply these methods in this setting. Time permitting, we will outline the exact method for computing the effective cones of these moduli spaces.