Connected Components of Hurwitz Spaces of Coverings with One Special Fiber and Monodromy Groups Contained in a Weyl Group of Type B d

Francesca Vetro

Bollettino dell'Unione Matematica Italiana (2008)

  • Volume: 1, Issue: 1, page 87-103
  • ISSN: 0392-4041

Abstract

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Let X , X ′ , Y be smooth projective complex curves with Y curve of genus ≥ 1 . Let d be an integer ≥ 3 , let e ¯ = ( e 1 , … , e r ) be a partition of d and let | e | = ∑ i = 1 r ( e i - 1 ) . Let X → 𝜋 X ′ → 𝑓 Y be a sequence of coverings where π is a degree 2 branched covering and f is a degree d covering, with monodromy group S d , branched in n 2 + 1 points, one of which is special point c whose local monodromy has cycle type given by e ¯ . Moreover the branch locus of the covering π is contained in f - 1 ⁢ ( c ) . In this paper we prove the irreducibility of the Hurwitz spaces that parameterize sequences of coverings as above with monodromy group a Weyl group of type D d when n 2 + | e ¯ | ≥ 2 ⁢ d . Besides we determine the connected components of the Hurwitz spaces that parameterize sequences of coverings as above but with monodromy group a Weyl group of type B d .

How to cite

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Vetro, Francesca. "Connected Components of Hurwitz Spaces of Coverings with One Special Fiber and Monodromy Groups Contained in a Weyl Group of Type $B_d$." Bollettino dell'Unione Matematica Italiana 1.1 (2008): 87-103. <http://eudml.org/doc/290460>.

@article{Vetro2008,
abstract = {Let $X$, $X'$, $Y$ be smooth projective complex curves with $Y$ curve of genus $\geq 1$. Let $d$ be an integer $\geq 3$, let $\underline\{e\} = (e_\{1\}, \ldots, e_\{r\})$ be a partition of $d$ and let $|e|= \sum_\{i=1\}^\{r\}(e_i - 1)$. Let $X \xrightarrow\{\pi\} X' \xrightarrow\{f\} Y$ be a sequence of coverings where $\pi$ is a degree 2 branched covering and $f$ is a degree $d$ covering, with monodromy group $S_d$, branched in $n_2 + 1$ points, one of which is special point $c$ whose local monodromy has cycle type given by $\underline\{e\}$. Moreover the branch locus of the covering $\pi$ is contained in $f^\{-1\} (c)$. In this paper we prove the irreducibility of the Hurwitz spaces that parameterize sequences of coverings as above with monodromy group a Weyl group of type $D_d$ when $n_2 +|\underline\{e\}| \geq 2d$. Besides we determine the connected components of the Hurwitz spaces that parameterize sequences of coverings as above but with monodromy group a Weyl group of type $B_d$.},
author = {Vetro, Francesca},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {2},
number = {1},
pages = {87-103},
publisher = {Unione Matematica Italiana},
title = {Connected Components of Hurwitz Spaces of Coverings with One Special Fiber and Monodromy Groups Contained in a Weyl Group of Type $B_d$},
url = {http://eudml.org/doc/290460},
volume = {1},
year = {2008},
}

TY - JOUR
AU - Vetro, Francesca
TI - Connected Components of Hurwitz Spaces of Coverings with One Special Fiber and Monodromy Groups Contained in a Weyl Group of Type $B_d$
JO - Bollettino dell'Unione Matematica Italiana
DA - 2008/2//
PB - Unione Matematica Italiana
VL - 1
IS - 1
SP - 87
EP - 103
AB - Let $X$, $X'$, $Y$ be smooth projective complex curves with $Y$ curve of genus $\geq 1$. Let $d$ be an integer $\geq 3$, let $\underline{e} = (e_{1}, \ldots, e_{r})$ be a partition of $d$ and let $|e|= \sum_{i=1}^{r}(e_i - 1)$. Let $X \xrightarrow{\pi} X' \xrightarrow{f} Y$ be a sequence of coverings where $\pi$ is a degree 2 branched covering and $f$ is a degree $d$ covering, with monodromy group $S_d$, branched in $n_2 + 1$ points, one of which is special point $c$ whose local monodromy has cycle type given by $\underline{e}$. Moreover the branch locus of the covering $\pi$ is contained in $f^{-1} (c)$. In this paper we prove the irreducibility of the Hurwitz spaces that parameterize sequences of coverings as above with monodromy group a Weyl group of type $D_d$ when $n_2 +|\underline{e}| \geq 2d$. Besides we determine the connected components of the Hurwitz spaces that parameterize sequences of coverings as above but with monodromy group a Weyl group of type $B_d$.
LA - eng
UR - http://eudml.org/doc/290460
ER -

References

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