Algebraic Geometry seminar by Roberto Svaldi - Tuesday 28 May at 11:00

[Jacopo Stoppa]

On Tuesday, 28 May at 11:00 in SISSA room 005 Roberto Svaldi (Statale
Milano) will give the seminar

"Towards a moduli theory for canonical models of foliated surfaces of
general type"

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 variational theory and the theory
of foliations, a whole cornucopia of new phenomena appears in the
latter. Accordingly, I will try to explain:
(1) what these new phenomena are;
(2) what new difficulties they introduce into the identification of a
good functor of moduli for the aforementioned foliations;
(3) how these difficulties can be overcome to obtain a satisfactory
theory of moduli and a construction of the associated moduli space for
foliated surfaces of general type.
The talk will feature joint work with C. Spicer, and joint work in
progress with M. McQuillan and Spicer.

Best,
Jacopo