Stable pair compactifications of the moduli space of degree one del pezzo surfaces via elliptic fibrations

Abstract

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 construct a stable pair compactification of the moduli space of anti-canonically polarized degree one del Pezzo surfaces.

Minor corrections and updated to reflect some changes in our paper on moduli of ellipic fibrations. Added figure to intro as well as a section comparing our construction with work of Heckman-Looijenga, and discussing connections with recent work of Laza-O'Grady