Alternative compactifications of the moduli space of curves

Abstract: The moduli space of curves is an important object in modern algebraic geometry, both interesting in its own right and serving as a test space for broader geometric programs. These often require the space to be compact, which leads to a variety of choices for compactification, the most well-known of which is the Deligne-Mumford-Knudsen compactification by stable curves, originally introduced in 1969. Since then, several alternative compactifications have been constructed and studied, and in 2013 David Smyth used a combinatorial framework to make progress towards classifying all "sufficiently nice" compactifications. In this talk, I'll discuss some of the most well-studied compactifications, as well as two new compactifications, which together classify the Gorenstein compactifications in genus 0 and genus 1.

algebraic geometrynumber theory

Audience: researchers in the topic

SFU NT-AG seminar

Series comments: The Number Theory and Algebraic Geometry (NT-AG) seminar is a research seminar dedicated to topics related to number theory and algebraic geometry hosted by the NT-AG group (Nils Bruin, Imin Chen, Stephen Choi, Katrina Honigs, Nathan Ilten, Marni Mishna).

We acknowledge the support of PIMS, NSERC, and SFU.

For Fall 2025, the organizers are Katrina Honigs and Peter McDonald.

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