Genus stabilization for moduli of curves with symmetries

2013/01/18 by Fabrizio Catanese, Catanese, Fabrizio, Michael Lönne +3
Mathematics · #14H10 #14H15 #14H30 #14H37 #20J06 #30F60 #55M35 #57M12 #57S05 #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #Complex Variables (math.CV) #FOS: Mathematics #math.AG #math.AT #math.CV #msc:14H10 #msc:14H15 #msc:14H30 #msc:14H37 #msc:20J06 #msc:30F60 #msc:55M35 #msc:57M12 #msc:57S05

paper · pdf · doi:10.48550/arxiv.1301.4409

21 pages, 2 figures

arxiv created 2013/01/18 · arxiv updated 2013/01/21

Abstract

In a previous paper, arXiv:1206.5498, we introduced a new homological invariant \e for the faithful action of a finite group G on an algebraic curve. We show here that the moduli space of curves admitting a faithful action of a finite group G with a fixed homological invariant \e, if the genus g' of the quotient curve is sufficiently large, is irreducible (and non empty iff the class satisfies the condition which we define as 'admissibility'). In the unramified case, a similar result had been proven by Dunfield and Thurston using the classical invariant in the second homology group of G, H₂(G, \ZZ). We achieve our result showing that the stable classes are in bijection with the set of admissible classes \e.

Citations

• The irreducible components of the moduli space of dihedral covers of algebraic curves

Related

• Genus stabilization for the homology of moduli spaces of orbit-framed curves with symmetries-I
• The irreducible components of the moduli space of dihedral covers of algebraic curves
• Twisted bundles and admissible covers
• Calculating cohomology groups of moduli spaces of curves via algebraic geometry
• Relations in the tautological ring of the moduli space of curves