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Speaker:

Helge Ruddat
Affiliation:

Universität Mainz
Date:

Wed, 2017-11-29 17:30 - 18:30
Location:

MPIM Lecture Hall Gross and Siebert gave an algorithm to produce from toric degeneration data a canonical formal

Calabi--Yau family. Siebert and I prove that this family is in fact the completion of an analytic

family. In particular, its nearby fibres are decent Calabi-Yau manifolds over the complex

numbers. Furthermore, the family is semi-universal, *i.e.* is in a sense locally the moduli

space of Calabi--Yaus. The key result on the route to analyticity is the computation of canonical

coordinates on the base by explicit integration of a holomorphic volume form over topological

cycles that we construct from tropical $1$-cycles in the base of the SYZ-fibration.

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