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math.AG2026

Basic properties of kappa classes

Valery Alexeev

We define kappa classes on KSBA moduli stacks as classes in operational Chow cohomology. They generalize the Miller-Morita-Mumford classes on the moduli spaces of curves. We prove…

math.AG2026

A tower of complete moduli spaces of Calabi-Yau -folds

Valery Alexeev

We construct a sequence of complete moduli spaces each of which is isomorphic to a weighted projective space. These…

math.AG2025

The KSBA moduli space of stable log Calabi-Yau surfaces

Valery Alexeev, Hülya Argüz, Pierrick Bousseau

We prove that every irreducible component of the coarse Kollár-Shepherd-Barron and Alexeev (KSBA) moduli space of stable log Calabi--Yau surfaces admits a finite cover by a projec…

math.AG2025

Compactifications of moduli spaces of K3 surfaces with a higher-order nonsymplectic automorphism

Valery Alexeev, Anand Deopurkar, Changho Han

We describe Baily-Borel, toroidal, and geometric -- using the KSBA stable pairs -- compactifications of some moduli spaces of K3 surfaces with a nonsymplectic automorphism of order…