Hyperelliptic limits of quadrics through canonical curves and ribbons

2019/05/28 by Alexander Polishchuk, Eric M. Rains, Polishchuk, Alexander +2
Computer Science · Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation #math.AG

paper · pdf · doi:10.48550/arxiv.1905.12113

31 pages

arxiv created 2019/05/28 · openalex publication_date 2019/05/28 · arxiv updated 2019/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe explicitly all hyperelliptic limits of quadrics through smooth canonical curves of genus g in \mathbb P^g-1. Also, we construct an open embedding of the blow up of a \rm PGL_g-bundle over the moduli space of curves of genus g along the hyperelliptic locus into the blow up of the canonical Hilbert scheme of \mathbb P^g-1 along the closure of the locus of canonical ribbons, which are certain double thickenings of rational normal curves introduced and studied by Bayer and Eisenbud.

Related

• Compactifying moduli of hyperelliptic curves
• Deforming a canonical curve inside a quadric
• Remarks on families of singular curves with hyperelliptic normalizations
• Most hyperelliptic curves over Q have no rational points
• Hyperelliptic curves and Ulrich sheaves on the complete intersection of two quadrics