Commensurabilities Among Lattices in Pu - Couverture rigide

Deligne, Pierre; Mostow, G. Daniel

Couverture rigide

ISBN 10 : 0691033854 ISBN 13 : 9780691033853

Editeur : Princeton University Press, 1993

Synopsis

The first part of this monograph is devoted to a characterization of hypergeometric-like functions, that is, twists of hypergeometric functions in n-variables. These are treated as an (n+1) dimensional vector space of multivalued locally holomorphic functions defined on the space of n+3 tuples of distinct points on the projective line P modulo, the diagonal section of Auto P=m. For n=1, the characterization may be regarded as a generalization of Riemann's classical theorem characterizing hypergeometric functions by their exponents at three singular points.


This characterization permits the authors to compare monodromy groups corresponding to different parameters and to prove commensurability modulo inner automorphisms of PU(1,n).


The book includes an investigation of elliptic and parabolic monodromy groups, as well as hyperbolic monodromy groups. The former play a role in the proof that a surprising number of lattices in PU(1,2) constructed as the fundamental groups of compact complex surfaces with constant holomorphic curvature are in fact conjugate to projective monodromy groups of hypergeometric functions. The characterization of hypergeometric-like functions by their exponents at the divisors "at infinity" permits one to prove generalizations in n-variables of the Kummer identities for n-1 involving quadratic and cubic changes of the variable.

A propos du livre

À propos de l?auteur

Pierre Deligne is a Permanent Member of the Department of Mathematics at the Institute for Advanced Study in Princeton. G. Daniel Mostow is Henry Ford II Professor of Mathematics at Yale University.

Détails de l'édition

• Éditeur: Princeton University Press
• Date d'édition: 1993
• Langue: anglais
• ISBN 10: 0691033854
• ISBN 13: 9780691033853
• Reliure: Relié
• Nombre de pages: 200
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible