Subcanonical points on algebraic curves

2010/02/16 by Evan M. Bullock, Bullock, Evan M. · 2 citations
Computer Science · Mathematics · #14H10 #14H55 (Primary) #32G15 (Secondary) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AG #msc:14H10 #msc:14H55 #msc:32G15

paper · pdf · doi:10.48550/arxiv.1002.2984

24 pages, 10 figures

openalex publication_date 2010/02/16 · arxiv created 2011/05/01 · arxiv updated 2011/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A point of an algebraic curve of genus g is subcanonical if some regular differential vanishes only at that point, with multiplicity 2g-2. Subcanonical points are Weierstrass points, and we compute the associated gap sequence at a general point of each component of the moduli space of curves with marked subcanonical point. We also construct subcanonical points with other gap sequences as ramification points of certain cyclic covers.

Cited by

• Locally non-trivial fibred surfaces with maximal unitary rank
• Irreducibility and stable rationality of the loci of Weierstrass points on curves of genus at most six

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• Minimal value set polynomials and a generalization of the Hermitian curve
• Extensions and paracanonical curves of genus 6
• Classes of Weierstrass points on genus 2 curves
• On the locus of curves with an odd subcanonical marked point