2014/09/16 by Helge Ruddat, Ruddat, Helge, Bernd Siebert +1 · 1 citation
Computer Science · Mathematics · #14H15 #14J32 #14J33 #14M25 #32G20 #32Q25 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1409.4750
openalex publication_date 2014/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that the mirror map is trivial for the canonical formal families of Calabi-Yau varieties constructed by Gross and the second author. 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. A side result is that the canonical formal families lift to analytic families. 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.