“Stable Pair Compactifications of the Moduli Space of Degree One del Pezzo Surface”

A degree one del Pezzo surface is the blowup of P^2 at 8 general points. By the classical Cayley-Bacharach Theorem, there is a unique 9th point whose blowup produces a rational elliptic surface with a section. Via this relationship, we can construct a stable pair compactification of the moduli space of anti-canonically polarized degree one del Pezzo surfaces. The KSBA theory of stable pairs (X,D) is the natural extension to dimension 2 of the Deligne-Mumford-Knudsen theory of stable curves. I will discuss the construction of the space of interest as a limit of a space of weighted stable elliptic surface pairs and explain how it relates to some previous compactifications of the space of degree one del Pezzo surfaces. This is joint work with Kenny Ascher.

### Details

Algebraic Geometry Seminar

Dori Bejleri (Brown)

May 18, 2018

3:00 PM -
4:00 PM

More information available at:

http://mathematics.stanford.edu/algebraic-geometry-seminar/ ### Location

Math 383-N

450 Serra Mall

Bldg. 380

Room 383-N

Stanford CA 94305