On the Hurwitz scheme and its monodromy

David Eisenbud; Noam Elkies; Joe Harris; Robert Speiser

Compositio Mathematica (1991)

  • Volume: 77, Issue: 1, page 95-117
  • ISSN: 0010-437X

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Eisenbud, David, et al. "On the Hurwitz scheme and its monodromy." Compositio Mathematica 77.1 (1991): 95-117. <http://eudml.org/doc/90068>.

@article{Eisenbud1991,
author = {Eisenbud, David, Elkies, Noam, Harris, Joe, Speiser, Robert},
journal = {Compositio Mathematica},
keywords = {isomorphic coverings; Tyrell conjecture; monodromy of the covering; Hurwitz scheme},
language = {eng},
number = {1},
pages = {95-117},
publisher = {Kluwer Academic Publishers},
title = {On the Hurwitz scheme and its monodromy},
url = {http://eudml.org/doc/90068},
volume = {77},
year = {1991},
}

TY - JOUR
AU - Eisenbud, David
AU - Elkies, Noam
AU - Harris, Joe
AU - Speiser, Robert
TI - On the Hurwitz scheme and its monodromy
JO - Compositio Mathematica
PY - 1991
PB - Kluwer Academic Publishers
VL - 77
IS - 1
SP - 95
EP - 117
LA - eng
KW - isomorphic coverings; Tyrell conjecture; monodromy of the covering; Hurwitz scheme
UR - http://eudml.org/doc/90068
ER -

References

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  2. A. Cayley, On the cubic curves inscribed in a given pencil of six lines. Quart J. of Pure and Appl. Math.9 (1868) 210-221. Zbl01.0168.01JFM01.0168.01
  3. A. Clebsch, Zur Theorie der binären Formen sechster Ordnung und zur Dreitheilung der hyperelliptischen Funktionen. Abh. der k. Ges. Wiss. zu Göttingen14 (1869) 1-59. 
  4. A. Clebsch: Zur Theorie der algebraischen Funktionen, Math. Ann.29 (1887) 171-186. MR1510409JFM19.0067.01
  5. D.B. Cohen: The Hurwitz monodromy group. J. Alg.32 (1974) 501-517. Zbl0343.20002MR387435
  6. S. Diaz and J. Harris: Geometry of the Severi Variety I, Trans. Am. Math. Soc. (1989). Zbl0677.14003
  7. J. Harris, Galois groups of enumerative problems. Duke J. Math.46 (1979) 685-724. Zbl0433.14040MR552521
  8. J. Harris and I. Morrison: Slopes of effective divisors on the moduli space of stable curves. Invent. Math. (to appear 1989). Zbl0705.14026MR1031904
  9. A. Hurwitz: Über Riemann'sche Flächen mit gegebenen Verzweigungspunkten. Math. Ann.39 (1891) 1-61. MR1510692JFM23.0429.01
  10. S. Kleiman and R. Speiser: Enumerative geometry of nonsingular plane cubics, submitted to the Proc. 1988 Sundance Conference. Contemporary Math. (to appear 1990.) Zbl0753.14045MR1108634
  11. P. Kluitmann: Hurwitz action and finite quotients of braid groups. In Braids, (Ed. J. S. Birman and A. Libgober), Contemporary Math.78, (1988) 299-325. Zbl0701.20019MR975086
  12. J. Lüroth, Note über Verzweigungsschnitte und Querschnitte in einer Riemann'schen Fläche. Math. Ann.4 (1871) 181-184. MR1509744JFM03.0192.02
  13. C. Maclachlan, On representations of Artin's Braid group. Mich. Math. J.25 (1978) 235-244. Zbl0366.20032MR494060
  14. S. Maillard, Recherche des charactéristiques des systèmes élémentaires de courbes planes du trosième ordre. Thèse, Paris, (1871), published by Cusset. JFM04.0305.02
  15. J.A. Tyrrell, Degenerate plane cubics and a theorem of Clebsch. Bull. London Math. Soc.5 (1973) 203-208. Zbl0268.14018MR347840

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