Commensurabilities among Lattices in PU (1,n). (AM-132), Volume 132 / / G. Daniel Mostow, Pierre Deligne

• Autore: Deligne Pierre
• Pubblicazione: Princeton, NJ : , : Princeton University Press, , [2016]; ©1994
• Descrizione fisica: 1 online resource (196 pages) : illustrations
• Disciplina: 515/.25
• Soggetto topico: Hypergeometric functions; Monodromy groups; Lattice theory
• Soggetto non controllato: Abuse of notation; Algebraic variety; Analytic continuation; Arithmetic group; Automorphism; Bernhard Riemann; Big O notation; Codimension; Coefficient; Cohomology; Commensurability (mathematics); Compactification (mathematics); Complete quadrangle; Complex number; Complex space; Conjugacy class; Connected component (graph theory); Coprime integers; Cube root; Derivative; Diagonal matrix; Differential equation; Dimension (vector space); Discrete group; Divisor (algebraic geometry); Divisor; Eigenvalues and eigenvectors; Ellipse; Elliptic curve; Equation; Existential quantification; Fiber bundle; Finite group; First principle; Fundamental group; Gelfand; Holomorphic function; Hypergeometric function; Hyperplane; Hypersurface; Integer; Inverse function; Irreducible component; Irreducible representation; Isolated point; Isomorphism class; Line bundle; Linear combination; Linear differential equation; Local coordinates; Local system; Locally finite collection; Mathematical proof; Minkowski space; Moduli space; Monodromy; Morphism; Multiplicative group; Neighbourhood (mathematics); Open set; Orbifold; Permutation; Picard group; Point at infinity; Polynomial ring; Projective line; Projective plane; Projective space; Root of unity; Second derivative; Simple group; Smoothness; Subgroup; Subset; Symmetry group; Tangent space; Tangent; Theorem; Transversal (geometry); Uniqueness theorem; Variable (mathematics); Vector space
• Persona (resp. second.): MostowG. Daniel
• Note generali: Bibliographic Level Mode of Issuance: Monograph
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: Frontmatter -- CONTENTS -- ACKNOWLEDGMENTS -- §1. INTRODUCTION -- §2. PICARD GROUP AND COHOMOLOGY -- §3. COMPUTATIONS FOR Q AND Q+ -- §4. LAURICELLA'S HYPERGEOMETRIC FUNCTIONS -- §5. GELFAND'S DESCRIPTION OF HYPERGEOMETRIC FUNCTIONS -- §6. STRICT EXPONENTS -- §7. CHARACTERIZATION OF HYPERGEOMETRIC-LIKE LOCAL SYSTEMS -- §8. PRELIMINARIES ON MONODROMY GROUPS -- §9. BACKGROUND HEURISTICS -- §10. SOME COMMENSURABILITY THEOREMS -- §11. ANOTHER ISOGENY -- §12. COMMENSURABILITY AND DISCRETENESS -- §13. AN EXAMPLE -- §14. ORBIFOLD -- §15. ELLIPTIC AND EUCLIDEAN μ'S, REVISITED -- §16. LIVNE'S CONSTRUCTION OF LATTICES IN PU(1,2) -- §17. LIN E ARRANGEMENTS: QUESTIONS -- Bibliography
• Sommario/riassunto: 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.
• Titolo autorizzato: Commensurabilities among Lattices in PU (1,n). (AM-132), Volume 132
• ISBN: 1-4008-8251-6
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910154745503321
• Lo trovi qui: Univ. Federico II
• Serie: Annals of mathematics studies ; ; no. 132.