Commensurabilities among Lattices in PU (1,n) (eBook)

Pierre R. Deligne, G. Daniel Mostow (Autoren)

eBook Download: PDF

2016
218 Seiten
Princeton University Press (Verlag)
978-1-4008-8251-9 (ISBN)

Infos

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.

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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 "e;at infinity"e; permits one to prove generalizations in n-variables of the Kummer identities for n-1 involving quadratic and cubic changes of the variable.

Produkt-Details

• Erscheint lt. Verlag: 2.3.2016
• Reihe/Serie: Annals of Mathematics Studies
• Reihe/Serie: Annals of Mathematics Studies
• Verlagsort: Princeton
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Schlagworte: 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 • Divisor (algebraic geometry) • 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 • Linear combination • linear differential equation • line bundle • Local coordinates • Locally finite collection • Local System • 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 • Tangent Space • Theorem • Transversal (geometry) • uniqueness theorem • Variable (mathematics) • Vector Space
• ISBN-10: 1-4008-8251-6 / 1400882516
• ISBN-13: 978-1-4008-8251-9 / 9781400882519