Residues and Gorenstein Contractions of Genus One Curves

Adrian Neff; Jonathan Wise

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arXiv · 2507.05326

Residues and Gorenstein Contractions of Genus One Curves

Adrian Neff·Jonathan Wise

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Abstract

Let $C$ be a genus one nodal curve over a local artinian base and let $E$ be a proper subcurve of genus one. We define residues for curves over local artinian rings, then define generalized residues with values in line bundles over the local artinian ring that arise from tropical data on the curve. We then use these residues to construct a contraction of $C$ that collapses $E$ to a Gorenstein genus one singularity.

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Adrian Neff, Jonathan Wise. 2025-07-07. Residues and Gorenstein Contractions of Genus One Curves. https://arxiv.org/abs/2507.05326

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