Residues and Gorenstein Contractions of Genus One Curves

2025/07/07 by Adrian Neff, Neff, Adrian, Jonathan Wise +1
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2507.05326

openalex publication_date 2025/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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.

Citations

• Gorenstein contractions of multiscale differentials

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