Modular Compactifications of M_{1,n} II

TL;DR

This paper establishes the projectivity of certain moduli spaces of n-pointed m-stable genus one curves and applies this to run a log minimal model program analogous to Hassett-Keel for these spaces.

Contribution

It proves the projectivity of moduli spaces of n-pointed m-stable genus one curves and demonstrates their use in a Hassett-Keel type minimal model program.

Findings

Moduli spaces of n-pointed m-stable curves are projective.

Application of these spaces to a Hassett-Keel type program.

Advancement in understanding the birational geometry of genus one moduli spaces.

Abstract

We prove that the moduli spaces of n-pointed m-stable curves introduced in our previous paper have projective coarse moduli. We use the resulting spaces to run an analogue of the Hassett-Keel log minimal model program for the moduli space of n-pointed stable curves of genus one.