Geometry and Physics Seminar: Helge Ruddat

Morrison defined canonical coordinates near a maximal degeneration point in the moduli of Calabi-Yau manifolds using Hodge theory. Gross and Siebert introduced a logarithmic-tropical algorithm to provide a canonically parametrized smoothing of a degenerate Calabi-Yau. We show that the Gross-Siebert coordinate is a canonical coordinate in the sense of Morrison. The coordinates are given by period integrals which we compute explicitly integrating over cycles constructed using tropical geometry. This is joint work with Siebert.