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arXiv · 2307.03947

Hyperelliptic Gorenstein curves and logarithmic differentials

Luca Battistella·Sebastian Bozlee
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Abstract

We produce a flexible tool for contracting subcurves of logarithmic hyperelliptic curves, which is local around the subcurve and commutes with arbitrary base-change. As an application, we prove that hyperelliptic multiscale differentials determine a sequence of Gorenstein contractions of the underlying nodal curve, whose dualising bundle they descend to generate. This is the first piece of evidence for a more general conjecture about limits of differentials.

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Luca Battistella, Sebastian Bozlee. 2023-07-08. Hyperelliptic Gorenstein curves and logarithmic differentials. https://doi.org/10.1017/fms.2024.76

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