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035   $a(DE-B1597)9781400882519
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100   $a20190708d2016      fg 
101 0 $aeng
135   $aurcnu||||||||
181   $ctxt
182   $cc
183   $acr
200 10$aCommensurabilities among Lattices in PU (1,n). (AM-132), Volume 132 /$fG. Daniel Mostow, Pierre Deligne
210  1$aPrinceton, NJ : $cPrinceton University Press, $d[2016]
210  4$d©1994
215   $a1 online resource (196 pages) $cillustrations
225 0 $aAnnals of Mathematics Studies ;$v313
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a0-691-00096-4 
311   $a0-691-03385-4 
320   $aIncludes bibliographical references.
327   $tFrontmatter -- $tCONTENTS -- $tACKNOWLEDGMENTS -- $t§1. INTRODUCTION -- $t§2. PICARD GROUP AND COHOMOLOGY -- $t§3. COMPUTATIONS FOR Q AND Q+ -- $t§4. LAURICELLA'S HYPERGEOMETRIC FUNCTIONS -- $t§5. GELFAND'S DESCRIPTION OF HYPERGEOMETRIC FUNCTIONS -- $t§6. STRICT EXPONENTS -- $t§7. CHARACTERIZATION OF HYPERGEOMETRIC-LIKE LOCAL SYSTEMS -- $t§8. PRELIMINARIES ON MONODROMY GROUPS -- $t§9. BACKGROUND HEURISTICS -- $t§10. SOME COMMENSURABILITY THEOREMS -- $t§11. ANOTHER ISOGENY -- $t§12. COMMENSURABILITY AND DISCRETENESS -- $t§13. AN EXAMPLE -- $t§14. ORBIFOLD -- $t§15. ELLIPTIC AND EUCLIDEAN ?'S, REVISITED -- $t§16. LIVNE'S CONSTRUCTION OF LATTICES IN PU(1,2) -- $t§17. LIN E ARRANGEMENTS: QUESTIONS -- $tBibliography
330   $aThe first part of this monograph is devoted to a characterization of hypergeometric-like functions, that is, twists of hypergeometric functions in n-variables. These are treated as an (n+1) dimensional vector space of multivalued locally holomorphic functions defined on the space of n+3 tuples of distinct points on the projective line P modulo, the diagonal section of Auto P=m. For n=1, the characterization may be regarded as a generalization of Riemann's classical theorem characterizing hypergeometric functions by their exponents at three singular points. This characterization permits the authors to compare monodromy groups corresponding to different parameters and to prove commensurability modulo inner automorphisms of PU(1,n). The book includes an investigation of elliptic and parabolic monodromy groups, as well as hyperbolic monodromy groups. The former play a role in the proof that a surprising number of lattices in PU(1,2) constructed as the fundamental groups of compact complex surfaces with constant holomorphic curvature are in fact conjugate to projective monodromy groups of hypergeometric functions. The characterization of hypergeometric-like functions by their exponents at the divisors "at infinity" permits one to prove generalizations in n-variables of the Kummer identities for n-1 involving quadratic and cubic changes of the variable.
410  0$aAnnals of mathematics studies ;$vno. 132.
606   $aHypergeometric functions
606   $aMonodromy groups
606   $aLattice theory
610   $aAbuse of notation.
610   $aAlgebraic variety.
610   $aAnalytic continuation.
610   $aArithmetic group.
610   $aAutomorphism.
610   $aBernhard Riemann.
610   $aBig O notation.
610   $aCodimension.
610   $aCoefficient.
610   $aCohomology.
610   $aCommensurability (mathematics).
610   $aCompactification (mathematics).
610   $aComplete quadrangle.
610   $aComplex number.
610   $aComplex space.
610   $aConjugacy class.
610   $aConnected component (graph theory).
610   $aCoprime integers.
610   $aCube root.
610   $aDerivative.
610   $aDiagonal matrix.
610   $aDifferential equation.
610   $aDimension (vector space).
610   $aDiscrete group.
610   $aDivisor (algebraic geometry).
610   $aDivisor.
610   $aEigenvalues and eigenvectors.
610   $aEllipse.
610   $aElliptic curve.
610   $aEquation.
610   $aExistential quantification.
610   $aFiber bundle.
610   $aFinite group.
610   $aFirst principle.
610   $aFundamental group.
610   $aGelfand.
610   $aHolomorphic function.
610   $aHypergeometric function.
610   $aHyperplane.
610   $aHypersurface.
610   $aInteger.
610   $aInverse function.
610   $aIrreducible component.
610   $aIrreducible representation.
610   $aIsolated point.
610   $aIsomorphism class.
610   $aLine bundle.
610   $aLinear combination.
610   $aLinear differential equation.
610   $aLocal coordinates.
610   $aLocal system.
610   $aLocally finite collection.
610   $aMathematical proof.
610   $aMinkowski space.
610   $aModuli space.
610   $aMonodromy.
610   $aMorphism.
610   $aMultiplicative group.
610   $aNeighbourhood (mathematics).
610   $aOpen set.
610   $aOrbifold.
610   $aPermutation.
610   $aPicard group.
610   $aPoint at infinity.
610   $aPolynomial ring.
610   $aProjective line.
610   $aProjective plane.
610   $aProjective space.
610   $aRoot of unity.
610   $aSecond derivative.
610   $aSimple group.
610   $aSmoothness.
610   $aSubgroup.
610   $aSubset.
610   $aSymmetry group.
610   $aTangent space.
610   $aTangent.
610   $aTheorem.
610   $aTransversal (geometry).
610   $aUniqueness theorem.
610   $aVariable (mathematics).
610   $aVector space.
615  0$aHypergeometric functions.
615  0$aMonodromy groups.
615  0$aLattice theory.
676   $a515/.25
700   $aDeligne$b Pierre, $042896
702   $aMostow$b G. Daniel, 
801  0$bDE-B1597
801  1$bDE-B1597
906   $aBOOK
912   $a9910154745503321
996   $aCommensurabilities among Lattices in PU (1,n). (AM-132), Volume 132$92785739
997   $aUNINA