A. Soldatenkov

activity

20242026

collaborators

5 papers

math.AG2026

Reflective lattices and hyperkahler manifolds

Ekaterina Amerik, Andrey Soldatenkov, Misha Verbitsky

Using the results of Nikulin and Vinberg on the groups of isometries generated by reflections, we construct a subvariety called the Nikulin-Vinberg locus in the moduli space of pol…

math.AG2025

The abundance and SYZ conjectures in families of hyperkahler manifolds

Andrey Soldatenkov, Misha Verbitsky

Let $L$ be a holomorphic line bundle on a hyperkahler manifold $M$ , with $c_{1} (L)$ nef and not big. SYZ conjecture predicts that $L$ is semiample. We prove that this is true, assumi…

math.AG2025

Birational geometry of hyperkahler manifolds and the Hu-Yau conjecture

Ekaterina Amerik, Andrey Soldatenkov, Misha Verbitsky

Wierzba and Wisniewski proved that in dimension 4, every bimeromorphic map of hyperkahler manifolds is represented as a composition of Mukai flops. Hu and Yau conjectured that this…

math.AG2025

Hermitian-symplectic and Kahler structures on degenerate twistor deformations

Andrey Soldatenkov, Misha Verbitsky

Let $(M, I^c ◯)$ be a holomorphically symplectic manifold equipped with a holomorphic Lagrangian fibration $I ¨ : M \to B$ , and $I^\cdot$ a closed $(1, 1)$ -form on $B$ . Then $I^c ◯ + I ¨ ^{*} I^\cdot$ is…

math.AG2024

Rigid currents on compact hyperkahler manifolds

Nessim Sibony, Andrey Soldatenkov, Misha Verbitsky

A rigid cohomology class on a complex manifold is a class that is represented by a unique closed positive current. The positive current representing a rigid class is also called ri…