Irreducibility of Hurwitz Spaces of Coverings with Monodromy Groups Weyl Groups of Type W ⁢ ( B d )

Francesca Vetro

Bollettino dell'Unione Matematica Italiana (2007)

  • Volume: 10-B, Issue: 2, page 405-431
  • ISSN: 0392-4041

Abstract

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Let Y be a smooth, connected, projective complex curve of genus > = 0. Biggers and Fried proved the irreducibility of the Hurwitz spaces which parametrize coverings of P 1 whose monodromy group is a Weyl of type W ⁢ ( B d ) . Here we prove the irreducibility of Hurwitz spaces that parametrize coverings of Y with monodromy group a Weyl group of type W ⁢ ( B d ) .

How to cite

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Vetro, Francesca. "Irreducibility of Hurwitz Spaces of Coverings with Monodromy Groups Weyl Groups of Type $W(B_d)$." Bollettino dell'Unione Matematica Italiana 10-B.2 (2007): 405-431. <http://eudml.org/doc/290359>.

@article{Vetro2007,
abstract = {Let Y be a smooth, connected, projective complex curve of genus > = 0. Biggers and Fried proved the irreducibility of the Hurwitz spaces which parametrize coverings of $P^1$whose monodromy group is a Weyl of type $W(B_d)$. Here we prove the irreducibility of Hurwitz spaces that parametrize coverings of Y with monodromy group a Weyl group of type $W(B_d)$.},
author = {Vetro, Francesca},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {6},
number = {2},
pages = {405-431},
publisher = {Unione Matematica Italiana},
title = {Irreducibility of Hurwitz Spaces of Coverings with Monodromy Groups Weyl Groups of Type $W(B_d)$},
url = {http://eudml.org/doc/290359},
volume = {10-B},
year = {2007},
}

TY - JOUR
AU - Vetro, Francesca
TI - Irreducibility of Hurwitz Spaces of Coverings with Monodromy Groups Weyl Groups of Type $W(B_d)$
JO - Bollettino dell'Unione Matematica Italiana
DA - 2007/6//
PB - Unione Matematica Italiana
VL - 10-B
IS - 2
SP - 405
EP - 431
AB - Let Y be a smooth, connected, projective complex curve of genus > = 0. Biggers and Fried proved the irreducibility of the Hurwitz spaces which parametrize coverings of $P^1$whose monodromy group is a Weyl of type $W(B_d)$. Here we prove the irreducibility of Hurwitz spaces that parametrize coverings of Y with monodromy group a Weyl group of type $W(B_d)$.
LA - eng
UR - http://eudml.org/doc/290359
ER -

References

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  1. BIGGERS, R. - FRIED, M., Moduli spaces for covers of P 1 and representations of the Hurwitz monodromy group, J. Reine Angew. Math., 335 (1982), 87-121. Zbl0484.14002MR667463
  2. BIGGERS, R. - FRIED, M., Irreducibility of moduli spaces of cyclic unramified covers of genus g curves, Trans. Amer. Math. Soc., 295, no. 1 (1986), 59-70. Zbl0601.14022MR831188DOI10.2307/2000145
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  8. GRABER, T. - HARRIS, J. - STARR, J., A note on Hurwitz schemes of covers of a positive genus curve, preprint, arXiv: math. AG/0205056. 
  9. HURWITZ, A., Ueber Riemann'schen Flächen mit gegebenen Verzweigungspunkten, Math. Ann., 39 (1891), 1-61. Zbl23.0429.01MR1510692DOI10.1007/BF01199469
  10. KANEV, V., Irreducibility of Hurwitz spaces, Preprint N. 241, February 2004, Dipartimento di Matematica ed Applicazioni, Università di Palermo; arXiv: math. AG/0509154. 
  11. KLUITMANN, P., Hurwitz action and finite quotients of braid groups, in: Braids (Santa Cruz, CA, 1986), in: Contemp. Math., 78, Amer. Math. Soc., Providence, RI, (1988), 299-325. MR975086DOI10.1090/conm/078/975086
  12. MOCHIZUKI, S., The geometry of the compactification of the Hurwitz Scheme, Publ. Res. Inst. Math. Sci., 31 (1995), 355-441. Zbl0866.14013MR1355945DOI10.2977/prims/1195164048
  13. NATANZON, S. M., Topology of 2-dimensional coverings and meromorphic functions on real and complex algebraic curves, Selected translations., Selecta Math. Soviet., 12, no. 3 (1993), 251-291. MR1244839
  14. SCOTT, G. P., Braid groups and the group of homeomorphisms of a surface, Proc. Cambrige Philos. Soc., 68 (1970), 605-617. Zbl0203.56302MR268889
  15. VETRO, F., Irreducibility of Hurwitz spaces of coverings with one special fiber, Indag. Mathem., 17, no. 1 (2006), 115-127. Zbl1101.14040MR2337168DOI10.1016/S0019-3577(06)80010-8
  16. VÖLKLEIN, H., Groups as Galois groups. An introduction, Cambridge Studies in Advances Mathematics, 53 (1996), Cambridge University Press MR1405612DOI10.1017/CBO9780511471117

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