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Andrey Soldatenkov ; Misha Verbitsky - The abundance and SYZ conjectures in families of hyperkahler manifolds
epiga:14370 - Épijournal de Géométrie Algébrique, December 9, 2025, Volume 9 - https://doi.org/10.46298/epiga.2025.14370The abundance and SYZ conjectures in families of hyperkahler manifoldsArticle
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.
17 pages, 2 figures, published version
Source: arXiv.org:2409.09142
Volume: Volume 9
Published on: December 9, 2025
Accepted on: July 13, 2025
Submitted on: September 30, 2024
Keywords: Algebraic Geometry, Differential Geometry, 53C26, 14J42
Classifications
Mathematics Subject Classification 20201
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