Roberto Svaldi : Towards a moduli theory for canonical models of foliated surfaces of general type

Posted by Philip Engel , part of the Algebraic Geometry Seminar.

At

Jan. 13, 2025, 3 p.m.

In

636 SEO

Abstract

In recent years there has been considerable progress in extending the ideas and techniques of the Minimal Model Program beyond the realm of algebraic varieties to the study of foliations. For the case of foliations on surfaces, McQuillan, Brunella and Mendes have obtained a detailed classification — analogous to the Enriques-Kodaira classification. In this seminar, I will explain how, using the birational classification of foliations on surfaces and MMP techniques, we can start constructing moduli spaces for minimal foliations that have maximum Kodaira dimension on surfaces. While there are many similarities between the birational theory and the theory of foliations, some new important phenomena appear in the latter. In the seminar, I will try to explain what these new phenomena are and what new difficulties they introduce into the identification of a good functor of moduli for the aforementioned foliations, in comparison to the case of KSBA moduli spaces. The talk will feature joint work with C. Spicer, and joint work in progress with M. McQuillan, C. Spicer, and S. Velazquez.