##### Department of Mathematics,

University of California San Diego

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### Math 208: Seminar in Algebraic Geometry

## Dr. Kristin DeVleming

#### UMass Amherst

## Moduli of boundary polarized Calabi-Yau pairs

##### Abstract:

I will discuss joint work with Kenny Ascher, Dori Bejleri, Harold Blum, Giovanni Inchiostro, Yuchen Liu, and Xiaowei Wang on construction of moduli stacks and moduli spaces of boundary polarized log Calabi Yau pairs. Unlike moduli of canonically polarized varieties (respectively, Fano varieties) in which the moduli stack of KSB stable (respectively, K semistable) objects is bounded for fixed volume, dimension, the objects here form unbounded families. Despite this unbounded behavior, we define the notion of asymptotically good moduli space, and, in the case of plane curve pairs (P2, C), we construct a projective good moduli space parameterizing S-equivalence classes of such pairs. Time permitting, I will discuss applications to the classification of special degenerations of P2, the b-semiampleness conjecture of Shokurov and Prokhorov, and the Hassett-Keel program.

Host: James McKernan

### December 1, 2023

### 3:00 PM

AP&M 7321

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