Published on *Max Planck Institute for Mathematics* (http://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Helge Ruddat
Affiliation:

Universität Mainz
Date:

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

**Links:**

[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] http://www.mpim-bonn.mpg.de/node/3444

[3] http://www.mpim-bonn.mpg.de/YRSM2017