Heights on curves and limits of Hodge structures
Spencer Bloch, Robin de Jong, Emre Can Sert\"oz
TL;DR
This paper establishes a detailed link between heights on algebraic curves and Hodge structures, proposing a novel method for computing complex heights in higher-dimensional algebraic geometry.
Contribution
It introduces a new connection between Néron–Tate heights and biextension heights of limit mixed Hodge structures, offering a fresh approach to height computations.
Findings
Connected heights on curves with Hodge structures.
Proposed a new method for higher-dimensional height calculations.
Provided insights into smoothing deformations of singular curves.
Abstract
We exhibit a precise connection between N\'eron--Tate heights on smooth curves and biextension heights of limit mixed Hodge structures associated to smoothing deformations of singular quotient curves. Our approach suggests a new way to compute Beilinson--Bloch heights in higher dimensions.
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