V. Alexeev

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math.AG2025

On the moduli space of stable surfaces with $p_{g} = 1$ realizing the minimal volume

Valery Alexeev, Wenfei Liu, Matthias Schütt

Let $M_{1}$ be the moduli space of the KSBA stable surfaces $X$ of geometric genus $p_{g} (X) = 1$ realizing the minimal possible volume $K_{X}^{2} = \frac{1}{143}$ . We show that its reduced part…

math.AG2025

Augmentations, reduced ideal point gluings and compact type degenerations of curves

Valery Alexeev, Alexander Kuznetsov

In this note we demonstrate some unexpected properties that simple gluings of the simplest derived categories may have. We consider two special cases: the first is an augmented cur…

math.AG2025

On lattice-polarized K3 surfaces

Valery Alexeev, Philip Engel

We propose modifications to the commonly used definitions of lattice-polarized and lattice-quasipolarized smooth K3 surfaces, collecting various versions of the definition, and det…

On the moduli space of stable surfaces with pg​=1 realizing the minimal volume

Augmentations, reduced ideal point gluings and compact type degenerations of curves

On lattice-polarized K3 surfaces

On the moduli space of stable surfaces with $p_{g} = 1$ realizing the minimal volume