Daebeom Choi : Birational Contractions of Mg,n and Their Dependence on the Characteristic

Posted by Eamon Quinlan-Gallego , part of the Algebraic Geometry Seminar.

At

April 13, 2026, 3 p.m.

In

636 SEO

Abstract

In this talk, we discuss the existence and nonexistence of certain birational contractions of \(\overline{\mathrm{M}}_{g,n}\). Somewhat surprisingly, this depends on the characteristic of the base field: many such contractions exist only in positive characteristic. We present a precise form of this phenomenon and discuss two examples that highlight the difference between characteristic zero and positive characteristic. The first is a simple and explicit contraction that exists only in positive characteristic, and the second is a modular interpretation of the morphisms associated with psi classes on \(\overline{\mathrm{M}}_{1,n}\). We also offer some speculation on why such characteristic-dependent phenomena arise.