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arXiv · 2510.24454

Birational geometry of hyperkahler manifolds and the Hu-Yau conjecture

Ekaterina Amerik·Andrey Soldatenkov·Misha Verbitsky
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Abstract

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 result can be generalized to arbitrary dimension. They defined ``Mukai's elementary transformation'' as the blow-up of a subvariety ruled by complex projective spaces, composed with the contraction of the ruling. Hu and Yau conjectured that any bimeromorphic map of hyperkahler manifolds can be decomposed into a sequence of Mukai's elementary transformations, after possibly removing subvarieties of codimension greater than $2$. We prove this conjecture for compact hyperkahler manifolds of maximal holonomy by decomposing any bimeromorphic map into a composition of wall-crossing flops associated with MBM contractions.

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Ekaterina Amerik, Andrey Soldatenkov, Misha Verbitsky. 2025-10-28. Birational geometry of hyperkahler manifolds and the Hu-Yau conjecture. https://arxiv.org/abs/2510.24454

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