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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.NT2025
Finite translation orbits on double families of abelian varieties (with an appendix by E. Amerik)
Ekaterina Amerik, Paolo Dolce, Francesco Tropeano
We study two families of -dimensional abelian varieties, induced by distinct rational maps defined on a common variety and mapping to two bases $\overlin…
math.AG2025
Parabolic automorphisms of hyperk{ä}hler manifolds: Orbits and Betti maps
Ekaterina Amerik, Serge Cantat
We study parabolic automorphisms of irreducible holomorphically symplectic manifolds with a lagrangian fibration. Such automorphisms are (possibly up to taking a power) fiberwise t…