A. Soldatenkov

activity

20222026

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

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.AG2024

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.AG2024

Hermitian-symplectic and Kahler structures on degenerate twistor deformations

Andrey Soldatenkov, Misha Verbitsky

Let $(M, Ω)$ be a holomorphically symplectic manifold equipped with a holomorphic Lagrangian fibration $π : M \to B$ , and $η$ a closed $(1, 1)$ -form on $B$ . Then $Ω + π^{*} η$ is a holo…

math.AG2022

Cohomology and André motives of hyperkähler orbifolds

Andrey Soldatenkov

One of the main tools for the study of compact hyperkähler manifolds is the natural action of the Looijenga-Lunts-Verbitsky Lie algebra on the cohomology of such manifolds. This al…