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Title:
Analyticity and Versality of Gross-Siebert families
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Abstract:
In a joint work with Siebert, I prove that the mirror map is trivial for the canonical formal families of Calabi-Yau varieties constructed by Gross and Siebert. In other words, the natural coordinate in a canonical Calabi-Yau family is a canonical coordinate in the sense of Hodge theory. This implies that the higher weight periods directly carry enumerative information with no further gauging necessary as opposed to the classical case. As a consequence, the canonical formal families lift to analytic families that are versal. We compute the relevant period integrals explicitly. The cycles to integrate over are constructed from tropical 1-cycles in the intersection complex of the degenerate Calabi-Yau
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