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: 0392-4033

Abstract

top
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

top

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

top
  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
  3. BIRMAN, J. S., On braid groups, Comm. Pure Appl. Math., 22 (1998), 41-72. Zbl0157.30904MR234447DOI10.1002/cpa.3160220104
  4. BOURBAKI, N., Groupes et algebres de Lie, Ch. 4-6, Éléments de Mathématique, 34 (1968), Hermann, Paris. MR573068
  5. CARTER, R. W., Conjugacy classes in the Weyl group, Compositio Math., 25 (1972), 1-59. Zbl0254.17005MR318337
  6. FADELL, E. - NEUWIRTH, L., Configuration spaces, Math. Scand., 10 (1962), 111-118. Zbl0136.44104MR141126DOI10.7146/math.scand.a-10517
  7. FULTON, W., Hurwitz Schemes and irreducibility of moduli of algebraic curves, Ann. of Math. (2), 10 (1969), 542-575. Zbl0194.21901MR260752DOI10.2307/1970748
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.