Mémoires de la Société Mathématique de France 2011; 219 pp; softcover Number: 125/126 ISBN10: 2856293336 ISBN13: 9782856293331 List Price: US$75 Member Price: US$60 Order Code: SMFMEM/125/126
 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 AbramovichCortiVistoli, HarrisMumford, and MochizukiWewers. 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 RiemannHurwitz formula, between these classes. Applications are given to the stack of cyclic covers of the projective line, with special attention to CornalbaHarris 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. Readership 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 ChevalleyWeil
 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
