Algebraic Geometry Seminar
Stable reduction of foliated surfaces
Speaker: Federico Buonerba, Courant Institute
Location: Warren Weaver Hall 317
Date: Tuesday, March 20, 2018, 3:30 p.m.
Synopsis:
In 1977 Bogomolov proved that on surfaces of general type
with c_1^2>c_2, curves of a given geometric genus
form a bounded family. The role played by foliations in his
proof was further investigated by McQuillan, who in 1998
proved the Green-Griffiths conjecture for the same class
of surfaces.
In this talk I will review some basic properties of foliations
on algebraic surfaces, with a focus on birational geometry as
initiated by Brunella, McQuillan and others.
I will then discuss the problem of their variation in families, and
present the main ideas behind the proof of the stable reduction
theorem in this context.