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arxiv: 2206.14474 · v3 · pith:LOYHLS2Anew · submitted 2022-06-29 · 🧮 math.AG · math.DG· math.NT

Special Lagrangian fibrations, Berkovich retraction, and crystallographic groups

Keita Goto , Yuji Odaka This is my paper
classification 🧮 math.AG math.DGmath.NT
keywords abelianberkovichcrystallographicexplicitlyfibrationsfinitegroupslagrangian
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We explicitly construct special Lagrangian fibrations on finite quotients of maximally degenerating abelian varieties, glue with Berkovich retraction in non-Archimedean geometry by using "hybrid" technique. We also study their symmetries explicitly which can be regarded as crystallographic groups. In particular, a conjecture of Kontsevich-Soibelman is solved at an enhanced level for finite quotients of abelian varieties in any dimension.

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    Assuming a canonical basis of the section ring satisfies valuative independence, the metric SYZ conjecture holds for polarised maximal degenerations of compact Calabi-Yau manifolds.