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.

arXiv commentMinor 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

References in corpus (2)

• Stable pair, tropical, and log canonical compact moduli of del Pezzo surfaces
• Explicit stable models of elliptic surfaces with sections

Cited by in corpus (2)

• Stable log surfaces, admissible covers, and canonical curves of genus 4
• The moduli space of rational elliptic surfaces of index two