Moduli of boundary polarized Calabi-Yau pairs

Abstract: While the theories of KSBA stability and K-stability have been successful in constructing compact moduli spaces of canonically polarized varieties and Fano varieties, respectively, the case of Calabi-Yau varieties remains less well understood. I will discuss a new approach to this problem in the case of boundary polarized Calabi-Yau pairs $(X,D)$, i.e. $X$ is a Fano variety and $D$ is an anticanonical $\mathbb{Q}$-divisor, in which we consider all semi-log-canonical degenerations. One challenge of this approach is that the moduli stack can be unbounded. Nevertheless, if we consider boundary polarized Calabi-Yau pairs as degenerations of $\mathbb{P}^2$ with plane curves, we show that there exists a projective good moduli space despite the unboundedness. This is joint work with K. Ascher, D. Bejleri, H. Blum, K. DeVleming, G. Inchiostro, and X. Wang.

algebraic geometrycombinatorics

Audience: researchers in the topic

Online Nottingham algebraic geometry seminar

Series comments: Online geometry seminar, typically held on Thursday. This seminar takes place online via Microsoft Teams on the Nottingham University "Algebraic Geometry" team.

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