The stable hyperelliptic locus in genus 3: An application of Porteous Formula

2013/10/21 by Eduardo Esteves, Esteves, Eduardo
Mathematics · #14H10 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14H10

paper · pdf · doi:10.48550/arxiv.1310.5561

arxiv created 2013/10/21 · arxiv updated 2013/10/22

Abstract

We compute the class of the closure of the locus of hyperelliptic curves in the moduli space of stable genus-3 curves in terms of the tautological class λ and the boundary classes δ₀ and δ₁. The expression of this class is known, but here we compute it directly, by means of Porteous Formula, without resorting to blowups or test curves.

Related

• The class of the bielliptic locus in genus 3
• On hyperelliptic curves of genus 3
• Loci of curves with subcanonical points in low genus
• Modifications of Hodge bundles and enumerative geometry : the stable hyperelliptic locus
• Genus 3 hyperelliptic curves with (2, 4, 4)-split Jacobians