Algebraic Geometry Seminar
Daniil Serebrennikov
Johns Hopkins University
Finiteness and Boundedness
Abstract: The Kawamata–Morrison cone conjecture is a long-standing problem in
birational geometry. Totaro generalized the conjecture and proved it
for klt Calabi–Yau pairs in dimension two. The conjecture predicts
that such a pair has only finitely many birational contractions modulo
its automorphism group. I will explain that the finiteness of the
targets of these contractions follows once they admit polarizations
of bounded degree. In dimension two, this provides a new proof of the
generalized Kawamata–Matsuki conjecture on the finiteness (up to log
isomorphism) of weak log canonical models within a birational class.
Monday January 12, 2026 at 3:00 PM in 636 SEO