Commensurabilities among Lattices in PU (1,n). (AM-132), Volume 132 / / G. Daniel Mostow, Pierre Deligne.
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 di...
Saved in:
Superior document: | Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 |
---|---|
VerfasserIn: | |
Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2016] ©1994 |
Year of Publication: | 2016 |
Language: | English |
Series: | Annals of Mathematics Studies ;
132 |
Online Access: | |
Physical Description: | 1 online resource (218 p.) |
Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
LEADER | 07672nam a22017295i 4500 | ||
---|---|---|---|
001 | 9781400882519 | ||
003 | DE-B1597 | ||
005 | 20220131112047.0 | ||
006 | m|||||o||d|||||||| | ||
007 | cr || |||||||| | ||
008 | 220131t20161994nju fo d z eng d | ||
020 | |a 9781400882519 | ||
024 | 7 | |a 10.1515/9781400882519 |2 doi | |
035 | |a (DE-B1597)467967 | ||
035 | |a (OCoLC)979747115 | ||
040 | |a DE-B1597 |b eng |c DE-B1597 |e rda | ||
041 | 0 | |a eng | |
044 | |a nju |c US-NJ | ||
050 | 4 | |a QA353.H9 | |
072 | 7 | |a MAT012040 |2 bisacsh | |
082 | 0 | 4 | |a 515/.25 |
100 | 1 | |a Deligne, Pierre, |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
245 | 1 | 0 | |a Commensurabilities among Lattices in PU (1,n). (AM-132), Volume 132 / |c G. Daniel Mostow, Pierre Deligne. |
264 | 1 | |a Princeton, NJ : |b Princeton University Press, |c [2016] | |
264 | 4 | |c ©1994 | |
300 | |a 1 online resource (218 p.) | ||
336 | |a text |b txt |2 rdacontent | ||
337 | |a computer |b c |2 rdamedia | ||
338 | |a online resource |b cr |2 rdacarrier | ||
347 | |a text file |b PDF |2 rda | ||
490 | 0 | |a Annals of Mathematics Studies ; |v 132 | |
505 | 0 | 0 | |t Frontmatter -- |t CONTENTS -- |t ACKNOWLEDGMENTS -- |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 μ'S, REVISITED -- |t §16. LIVNE'S CONSTRUCTION OF LATTICES IN PU(1,2) -- |t §17. LIN E ARRANGEMENTS: QUESTIONS -- |t Bibliography |
506 | 0 | |a restricted access |u http://purl.org/coar/access_right/c_16ec |f online access with authorization |2 star | |
520 | |a 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. | ||
530 | |a Issued also in print. | ||
538 | |a Mode of access: Internet via World Wide Web. | ||
546 | |a In English. | ||
588 | 0 | |a Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) | |
650 | 0 | |a Hypergeometric functions. | |
650 | 0 | |a Lattice theory. | |
650 | 0 | |a Monodromy groups. | |
650 | 7 | |a MATHEMATICS / Geometry / Non-Euclidean. |2 bisacsh | |
653 | |a Abuse of notation. | ||
653 | |a Algebraic variety. | ||
653 | |a Analytic continuation. | ||
653 | |a Arithmetic group. | ||
653 | |a Automorphism. | ||
653 | |a Bernhard Riemann. | ||
653 | |a Big O notation. | ||
653 | |a Codimension. | ||
653 | |a Coefficient. | ||
653 | |a Cohomology. | ||
653 | |a Commensurability (mathematics). | ||
653 | |a Compactification (mathematics). | ||
653 | |a Complete quadrangle. | ||
653 | |a Complex number. | ||
653 | |a Complex space. | ||
653 | |a Conjugacy class. | ||
653 | |a Connected component (graph theory). | ||
653 | |a Coprime integers. | ||
653 | |a Cube root. | ||
653 | |a Derivative. | ||
653 | |a Diagonal matrix. | ||
653 | |a Differential equation. | ||
653 | |a Dimension (vector space). | ||
653 | |a Discrete group. | ||
653 | |a Divisor (algebraic geometry). | ||
653 | |a Divisor. | ||
653 | |a Eigenvalues and eigenvectors. | ||
653 | |a Ellipse. | ||
653 | |a Elliptic curve. | ||
653 | |a Equation. | ||
653 | |a Existential quantification. | ||
653 | |a Fiber bundle. | ||
653 | |a Finite group. | ||
653 | |a First principle. | ||
653 | |a Fundamental group. | ||
653 | |a Gelfand. | ||
653 | |a Holomorphic function. | ||
653 | |a Hypergeometric function. | ||
653 | |a Hyperplane. | ||
653 | |a Hypersurface. | ||
653 | |a Integer. | ||
653 | |a Inverse function. | ||
653 | |a Irreducible component. | ||
653 | |a Irreducible representation. | ||
653 | |a Isolated point. | ||
653 | |a Isomorphism class. | ||
653 | |a Line bundle. | ||
653 | |a Linear combination. | ||
653 | |a Linear differential equation. | ||
653 | |a Local coordinates. | ||
653 | |a Local system. | ||
653 | |a Locally finite collection. | ||
653 | |a Mathematical proof. | ||
653 | |a Minkowski space. | ||
653 | |a Moduli space. | ||
653 | |a Monodromy. | ||
653 | |a Morphism. | ||
653 | |a Multiplicative group. | ||
653 | |a Neighbourhood (mathematics). | ||
653 | |a Open set. | ||
653 | |a Orbifold. | ||
653 | |a Permutation. | ||
653 | |a Picard group. | ||
653 | |a Point at infinity. | ||
653 | |a Polynomial ring. | ||
653 | |a Projective line. | ||
653 | |a Projective plane. | ||
653 | |a Projective space. | ||
653 | |a Root of unity. | ||
653 | |a Second derivative. | ||
653 | |a Simple group. | ||
653 | |a Smoothness. | ||
653 | |a Subgroup. | ||
653 | |a Subset. | ||
653 | |a Symmetry group. | ||
653 | |a Tangent space. | ||
653 | |a Tangent. | ||
653 | |a Theorem. | ||
653 | |a Transversal (geometry). | ||
653 | |a Uniqueness theorem. | ||
653 | |a Variable (mathematics). | ||
653 | |a Vector space. | ||
700 | 1 | |a Mostow, G. Daniel, |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t Princeton Annals of Mathematics eBook-Package 1940-2020 |z 9783110494914 |o ZDB-23-PMB |
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t Princeton University Press eBook-Package Archive 1927-1999 |z 9783110442496 |
776 | 0 | |c print |z 9780691000961 | |
856 | 4 | 0 | |u https://doi.org/10.1515/9781400882519 |
856 | 4 | 0 | |u https://www.degruyter.com/isbn/9781400882519 |
856 | 4 | 2 | |3 Cover |u https://www.degruyter.com/document/cover/isbn/9781400882519/original |
912 | |a 978-3-11-044249-6 Princeton University Press eBook-Package Archive 1927-1999 |c 1927 |d 1999 | ||
912 | |a EBA_BACKALL | ||
912 | |a EBA_CL_MTPY | ||
912 | |a EBA_EBACKALL | ||
912 | |a EBA_EBKALL | ||
912 | |a EBA_ECL_MTPY | ||
912 | |a EBA_EEBKALL | ||
912 | |a EBA_ESTMALL | ||
912 | |a EBA_PPALL | ||
912 | |a EBA_STMALL | ||
912 | |a GBV-deGruyter-alles | ||
912 | |a PDA12STME | ||
912 | |a PDA13ENGE | ||
912 | |a PDA18STMEE | ||
912 | |a PDA5EBK | ||
912 | |a ZDB-23-PMB |c 1940 |d 2020 |