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].
Vetro, F. (2006). Irreducibility of Hurwitz spaces of coverings with one special fiber. INDAGATIONES MATHEMATICAE, 17(1), 115-127 [10.1016/S0019-3577(06)80010-8].
Data di pubblicazione: | 2006 | |
Titolo: | Irreducibility of Hurwitz spaces of coverings with one special fiber | |
Autori: | ||
Citazione: | Vetro, F. (2006). Irreducibility of Hurwitz spaces of coverings with one special fiber. INDAGATIONES MATHEMATICAE, 17(1), 115-127 [10.1016/S0019-3577(06)80010-8]. | |
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Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/S0019-3577(06)80010-8 | |
Appare nelle tipologie: | 1.01 Articolo in rivista |
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