Genus stabilization for the components of moduli spaces of curves with symmetries

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Autoren

  • Fabrizio Catanese
  • Michael Lönne
  • Fabio Perroni

Organisationseinheiten

Externe Organisationen

  • Scuola Internazionale Superiore di Studi Avanzati
  • Universität Bayreuth
Forschungs-netzwerk anzeigen

Details

OriginalspracheEnglisch
Seiten (von - bis)23-49
Seitenumfang27
FachzeitschriftAlgebraic Geometry
Jahrgang3
Ausgabenummer1
PublikationsstatusVeröffentlicht - 1 Jan. 2016

Abstract

In a previous paper (Groups, Geometry, and Dynamics, 2015), we introduced a new homological invariant ε 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 ε, if the genus g' of the quotient curve satisfies g' » 0, is irreducible (and non-empty if and only if the class satisfies the 'admissibility' condition). We achieve this by showing that the stable equivalence classes of Hurwitz generating systems are in bijection with the admissible classes ε.

Zitieren

Genus stabilization for the components of moduli spaces of curves with symmetries. / Catanese, Fabrizio; Lönne, Michael; Perroni, Fabio.
in: Algebraic Geometry, Jahrgang 3, Nr. 1, 01.01.2016, S. 23-49.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Catanese F, Lönne M, Perroni F. Genus stabilization for the components of moduli spaces of curves with symmetries. Algebraic Geometry. 2016 Jan 1;3(1):23-49. doi: 10.48550/arXiv.1301.4409, 10.14231/AG-2016-002
Catanese, Fabrizio ; Lönne, Michael ; Perroni, Fabio. / Genus stabilization for the components of moduli spaces of curves with symmetries. in: Algebraic Geometry. 2016 ; Jahrgang 3, Nr. 1. S. 23-49.
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