2022/05/17 by A. J. Parameswaran, Parameswaran, A. J., Amith Shastri K +1
Computer Science · Mathematics · #14H20 #14H40 #14L15 #Advanced Differential Equations and Dynamical Systems #Affine transformation #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Applied mathematics #FOS: Mathematics #Gravitational singularity #Group Theory (math.GR) #Jacobian matrix and determinant #Mathematical analysis #Mathematics #Normalization (sociology) #Polynomial and algebraic computation #Pure mathematics #Singular point of a curve #Torsion (gastropod) #math.AG #math.GR #msc:14H20 #msc:14H40 #msc:14L15
paper · pdf · doi:10.48550/arxiv.2205.08522
published in arXiv (Cornell University) (Cornell University) · 16 pages, comments and suggestions are welcome! Minor corrections and typos. Added acknowledgements
openalex publication_date 2022/05/17 · arxiv created 2022/05/19 · arxiv updated 2022/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We give criteria for the Jacobian of a singular curve X with at most ordinary n-point singularities to be anti-affine. In particular, for the case of curves with single ordinary double point we exhibit a relation with torsion divisors. If the geometric genus of the singular curve is atleast 3 and the normalization is non-hyperelliptic and non-bielliptic, then except for finitely many cases the Jacobian of X is anti-affine. Furthermore, if the normalization is a general curve of genus atleast 3 then the Jacobian of X is always anti-affine.