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Special Lagrangian fibrations, Berkovich retraction, and crystallographic groups.(English)Zbl 1537.81065

Summary: We explicitly construct special Lagrangian fibrations on finite quotients of maximally degenerating abelian varieties and glue these to the Berkovich retraction to form a “hybrid” fibration. We also study their symmetries explicitly that can be regarded as crystallographic groups. In particular, a conjecture of Kontsevich-Soibelman [Y. Liu, J. Differ. Geom. 89, No. 1, 87–110 (2011;Zbl 1254.14026), Conjecture 3] is solved at an enhanced level for finite quotients of abelian varieties in any dimension.

MSC:

81P68 Quantum computation
70H03 Lagrange’s equations
14D10 Arithmetic ground fields (finite, local, global) and families or fibrations
14L30 Group actions on varieties or schemes (quotients)
20H15 Other geometric groups, including crystallographic groups
14K05 Algebraic theory of abelian varieties

Citations:

Zbl 1254.14026

Cite

References:

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This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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