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Champs de Hurwitz
J. Bertin and M. Romagny, University Pierre et Marie Curie, Paris, France
A publication of the Société Mathématique de France.
Mémoires de la Société Mathématique de France
2011; 219 pp; softcover
Number: 125/126
ISBN-10: 2-85629-333-6
ISBN-13: 978-2-85629-333-1
List Price: US$75
Member Price: US$60
Order Code: SMFMEM/125/126
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In this work, the authors give a thorough study of Hurwitz stacks and associated Hurwitz moduli spaces, both in the Galois and the non- Galois case, with particular attention to correspondances between these moduli spaces. They compare their construction to those proposed by Abramovich-Corti-Vistoli, Harris-Mumford, and Mochizuki-Wewers. They apply their results to revisit some classical examples, particularly the stacks of stable curves equipped with an arbitrary level structure, and the stacks of tamely ramified cyclic covers. In a second part they exhibit some tautological bundles and cohomology classes naturally living on Hurwitz stacks, and give some universal relations, in particular a higher analogue of the Riemann-Hurwitz formula, between these classes. Applications are given to the stack of cyclic covers of the projective line, with special attention to Cornalba-Harris type relations and to cyclic, in particular hyperelliptic Hodge integrals.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.


Graduate students and research mathematicians interested in pure mathematics, algebra, and algebraic geometry.

Table of Contents

  • Introduction
  • Classification des revêtements
  • Familles de \(G\)-courbes lisses et Théorème de Chevalley-Weil
  • Familles de \(G\)-courbes stables
  • Déformations des revêtements modérément ramifiés
  • Champs de Hurwitz
  • Graphes et revêtements
  • Structures de niveau sur les courbes stables
  • Revêtements cycliques
  • Classes tautologiques
  • Index
  • Bibliographie
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