Algebraic Geometry Seminar: Finiteness and Boundedness, by Daniil Serebrennikov
January 12, 2026
3:00 PM - 3:50 PM
Daniil Serebrennikov (Johns Hopkins University): Finiteness and Boundedness
The KawamataMorrison cone conjecture is a long-standing problem in
birational geometry. Totaro generalized the conjecture and proved it
for klt CalabiYau 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 KawamataMatsuki conjecture on the finiteness (up to log
isomorphism) of weak log canonical models within a birational class.
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Date posted
Jan 23, 2026
Date updated
Jan 23, 2026
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