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arXiv · 2409.09142

The abundance and SYZ conjectures in families of hyperkahler manifolds

Andrey Soldatenkov·Misha Verbitsky
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Abstract

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, assuming that $(M,L)$ has a deformation $(M',L')$ with $L'$ semiample. We introduce a version of the Teichmuller space that parametrizes pairs $(M,L)$ up to isotopy. We prove a version of the global Torelli theorem for such Teichmuller spaces and use it to deduce the deformation invariance of semiampleness.

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Andrey Soldatenkov, Misha Verbitsky. 2024-09-13. The abundance and SYZ conjectures in families of hyperkahler manifolds. https://doi.org/10.46298/epiga.2025.14370

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