The abundance and SYZ conjectures in families of hyperkahler manifolds

2024/09/13 by Andrey Soldatenkov, Misha Verbitsky · 2 citations
Mathematics · #math.AG #math.DG

paper · pdf · doi:10.46298/epiga.2025.14370

Abstract

Let L be a holomorphic line bundle on a hyperkahler manifold M, with c₁(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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• Teichmüller spaces and Torelli theorems for hyperkähler manifolds
• A hyperholomorphic line bundle on certain hyperkähler manifolds not admitting an S¹-symmetry
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• Some density results for hyperkähler manifolds