Quelques remarques sur le champ des courbes hyperelliptiques en caracteristique deux

2004/11/17 by Jose Bertin, Bertin, Jose
Mathematics · #14A20 #14C22 #14D20 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14A20 #msc:14C22 #msc:14D20

paper · pdf · doi:10.48550/arxiv.math/0411382

novembre 2004

arxiv created 2004/11/17 · arxiv updated 2009/12/01

Abstract

Dans cette note on decrit le champ des courbes hyperelliptiques lisses defines sur un corps algebriquement clos de caracteristique deux comme un champ quotient. On en deduit le groupe de Picard. ----- In this note we describe the stack \cal H_g of smooth hyperelliptic curves of genus g over an algebraically closed field of characteristic two, as a quotient stack of a smooth variety of dimension 3g+5 by a non reductive algebraic group, extending a well known result of Vistoli. As an application, we show the Mumford-Vistoli description of the Picard group of the stack \cal H_g is valid in this characteristic. We also describe the natural stratification of \cal H_g by means of higher ramification data. We point out that after stable compactification \cal H_g is not smooth in codimension at least two.

Related

• The 2-ranks of Hyperelliptic Curves with Extra Automorphisms
• A complete description of the cohomological invariants of even genus hyperelliptic curves
• Compactified Picard stacks over \mathcal M_g
• Families of hyperelliptic curves
• The Chow ring of the universal Picard stack over the hyperelliptic locus