On the Bielliptic and bihyperelliptic loci

2018/07/05 by Frediani, Paola, Porru, Paola · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1807.02073

Abstract

We study some particular loci inside the moduli space M_g, namely the bielliptic locus (i.e. the locus of curves admitting a 2:1 cover over an elliptic curve E) and the bihyperelliptic locus (i.e. the locus of curves admitting a 2:1 cover over a hyperelliptic curve C', g(C') ≥ 2). We show that the bielliptic locus is not a totally geodesic subvariety of A_g if g ≥ 4 (while it is for g=3, see [16]) and that the bihyperelliptic locus is not totally geodesic in A_g if g ≥ 3g'. We also give a lower bound for the rank of the second gaussian map on the generic point of the bielliptic locus and an upper bound for this rank for every bielliptic curve.

Cited by

• Families of cyclic curve coverings with maximal monodromy

Related

• The class of the bielliptic locus in genus 3
• The bielliptic locus in the Hilbert scheme of canonical curves is unirational
• Loci of curves with subcanonical points in low genus
• Hyperelliptic curves covering an elliptic curve twice
• Higher Gaussian maps on the hyperelliptic locus and second fundamental form