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Семинар отдела алгебры и отдела алгебраической геометрии (семинар И. Р. Шафаревича)
15 июня 2021 г. 15:00, г. Москва, МИАН, комн. 104 (ул. Губкина, 8) + Zoom


Compact moduli of K3 surfaces

V. A. Alexeev

Аннотация: Let $F$ be a moduli space of lattice-polarized 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.

Язык доклада: английский


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