Pierre Deligne

(Author)

Commensurabilities Among Lattices in Pu (1, N). (Am-132), Volume 132Paperback, 12 September 1993

Commensurabilities Among Lattices in Pu (1, N). (Am-132), Volume 132
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Part of Series
Annals of Mathematics Studies
Part of Series
Annals of Mathematics Studies (Paperback)
Part of Series
Annals of Mathematics Studies, 132
Print Length
218 pages
Language
English
Publisher
Princeton University Press
Date Published
12 Sep 1993
ISBN-10
0691000964
ISBN-13
9780691000961

Description

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.

Product Details

Authors:
Pierre DeligneG Daniel Mostow
Book Format:
Paperback
Country of Origin:
US
Date Published:
12 September 1993
Dimensions:
23.42 x 15.44 x 1.32 cm
ISBN-10:
0691000964
ISBN-13:
9780691000961
Language:
English
Location:
Princeton
Pages:
218
Weight:
272.16 gm

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