Irreducibility of Hurwitz spaces of coverings with one special fiber

Francesca Vetro, Francesca Vetro

    Risultato della ricerca: Articlepeer review

    15 Citazioni (Scopus)

    Abstract

    Let Y be a smooth, projective complex curve of genus g ≥ 1. Let d be an integer ≥ 3, let e = {e1, e2,..., er} be a partition of d and let |e| = Σi=1r(ei - 1). In this paper we study the Hurwitz spaces which parametrize coverings of degree d of Y branched in n points of which n - 1 are points of simple ramification and one is a special point whose local monodromy has cyclic type e and furthermore the coverings have full monodromy group Sd. We prove the irreducibility of these Hurwitz spaces when n - 1 + |e| ≥ 2d, thus generalizing a result of Graber, Harris and Starr [A note on Hurwitz schemes of covers of a positive genus curve, Preprint, math. AG/0205056].
    Lingua originaleEnglish
    pagine (da-a)115-127
    Numero di pagine13
    RivistaIndagationes Mathematicae
    Volume17
    Stato di pubblicazionePublished - 2006

    All Science Journal Classification (ASJC) codes

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