EVENT DETAILS AND ABSTRACT

Title: Moduli of weighted stable marked del Pezzo surfaces
Speaker: Nolan Schock
Speaker Info: UIC
Brief Description:
Special Note:
Abstract:

The moduli space of marked del Pezzo surfaces is one of the most classical moduli spaces in algebraic geometry, essentially dating back to Cayley's original study of the 27 lines on a cubic surface. I will discuss an approach to compactifying the moduli space of marked del Pezzo surfaces via KSBA weighted stable pairs (S,aB), the natural higher dimensional generalizations of Hassett's moduli of weighted stable n-pointed curves. When the degree of the del Pezzo surface is 3 or 4, the compactification of interest is explicitly described when a=1 by work of Hacking, Keel, and Tevelev. In these cases we describe the complete sequence of wall crossings as one decreases the weight a from 1 to the smallest value such that (S,aB) is still a stable pair. Time permitting, I will also discuss potential generalizations to smaller weights and lower degree del Pezzo surfaces.