Emre Sertöz - Limit periods, arithmetic, and combinatorics - 16.06.2023

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Hodge theory, Mirror Symmetry, and Physics of Calabi-Yau Moduli
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A MATCH-PIMS-STRUCTURES workshop in Mathematical Physics, held from June 12 to 16, 2023, at the Mathematikon in Heidelberg
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Abstract: With Spencer Bloch and Robin de Jong, we recently proved that in a nodal degeneration of smooth curves, the periods of the resulting limit mixed Hodge structure (LMHS) contain arithmetic information. In particular, if the nodal fiber is identified with a smooth curve C glued at two points pp and qq then the LMHS relates to the Neron-Tate height of p−q in the Jacobian of C. In making this relation precise, we observed that a "tropical correction term" is required that is based on the finite reductions of the degenerate fiber. In this talk, I will explain this circle of ideas with the goal of arriving at the tropical correction term.