

Shafarevich Seminar
June 15, 2021 15:00, Moscow, Steklov Mathematical Institute, Room. 104 (8 Gubkina) + Zoom






Compact moduli of K3 surfaces
V. A. Alexeev^{} 
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Abstract:
Let $F$ be a moduli space of
latticepolarized K3 surfaces. Suppose that one has chosen a
canonical effective ample divisor $R$ on a general K3 in $F$. We call
this divisor "recognizable" if its flat limit on Kulikov surfaces is
well defined. We prove that the normalization of the stable pair
compactification $F_R$ for a recognizable divisor is a Looijenga
semitoroidal compactification. For polarized K3 surfaces $(X,L)$ of
degree $2d$, we show that the sum of rational curves in the linear
system $L$ is a recognizable divisor, giving a modular semitoroidal
compactification of $F_{2d}$ for all $d$.
This is a joint work with Philip Engel.
Language: English

