MARC Record from marc_columbia

LEADER: 06154mam a2200361 a 4500
001 3305975
005 20221020033655.0
008 020524t20022002riu b 001 0 eng d
010 $a 2002018346
020 $a082183178X (alk. paper)
035 $a(OCoLC)ocm49862239
035 $9AUU5465CU
035 $a(NNC)3305975
035 $a3305975
040 $aTEF$cTEF$dOrLoB-B
050 4 $aQA331.7$b.T39 2002
100 1 $aTaylor, Joseph L.,$d1941-2016.$0http://id.loc.gov/authorities/names/n2002017372
245 10 $aSeveral complex variables with connections to algebraic geometry and lie groups /$cJoseph L. Taylor.
260 $aProvidence, R.I. :$bAmerican Mathematical Society,$c[2002], ©2002.
300 $axvi, 507 pages ;$c27 cm.
336 $atext$btxt$2rdacontent
337 $aunmediated$bn$2rdamedia
490 1 $aGraduate studies in mathematics,$x1065-7339 ;$vv. 46
504 $aIncludes bibliographical references (p. 497-499) and index.
505 00 $gCh. 1.$tSelected Problems in One Complex Variable.$g1.1.$tPreliminaries.$g1.2.$tA Simple Problem.$g1.3.$tPartitions of Unity.$g1.4.$tThe Cauchy-Riemann Equations.$g1.5.$tThe Proof of Proposition 1.2.2.$g1.6.$tThe Mittag-Leffler and Weierstrass Theorems.$g1.7.$tConclusions and Comments --$gCh. 2.$tHolomorphic Functions of Several Variables.$g2.1.$tCauchy's Formula and Power Series Expansions.$g2.2.$tHartog's Theorem.$g2.3.$tThe Cauchy-Riemann Equations.$g2.4.$tConvergence Theorems.$g2.5.$tDomains of Holomorphy --$gCh. 3.$tLocal Rings and Varieties.$g3.1.$tRings of Germs of Holomorphic Functions.$g3.2.$tHilbert's Basis Theorem.$g3.3.$tThe Weierstrass Theorems.$g3.4.$tThe Local Ring of Holomorphic Functions is Noetherian.$g3.5.$tVarieties.$g3.6.$tIrreducible Varieties.$g3.7.$tImplicit and Inverse Mapping Theorems.$g3.8.$tHolomorphic Functions on a Subvariety --$gCh. 4.$tThe Nullstellensatz.$g4.1.$tReduction to the Case of Prime Ideals.$g4.2.$tSurvey of Results on Ring and Field Extensions.
505 80 $g4.3.$tHilbert's Nullstellensatz.$g4.4.$tFinite Branched Holomorphic Covers.$g4.5.$tThe Nullstellensatz.$g4.6.$tMorphisms of Germs of Varieties --$gCh. 5.$tDimension.$g5.1.$tTopological Dimension.$g5.2.$tSubvarieties of Codimension 1.$g5.3.$tKrull Dimension.$g5.4.$tTangential Dimension.$g5.5.$tDimension and Regularity.$g5.6.$tDimension of Algebraic Varieties.$g5.7.$tAlgebraic vs. Holomorphic Dimension --$gCh. 6.$tHomological Algebra.$g6.1.$tAbelian Categories.$g6.2.$tComplexes.$g6.3.$tInjective and Projective Resolutions.$g6.4.$tHigher Derived Functors.$g6.5.$tExt.$g6.6.$tThe Category of Modules, Tor.$g6.7.$tHilbert's Syzygy Theorem --$gCh. 7.$tSheaves and Sheaf Cohomology.$g7.1.$tSheaves.$g7.2.$tMorphisms of Sheaves.$g7.3.$tOperations on Sheaves.$g7.4.$tSheaf Cohomology.$g7.5.$tClasses of Acyclic Sheaves.$g7.6.$tRinged Spaces.$g7.7.$tDe Rham Cohomology.$g7.8.$tCech Cohomology.$g7.9.$tLine Bundles and Cech Cohomology --$gCh. 8.$tCoherent Algebraic Sheaves.$g8.1.$tAbstract Varieties.$g8.2.$tLocalization.
505 80 $g8.3.$tCoherent and Quasi-coherent Algebraic Sheaves.$g8.4.$tTheorems of Artin-Rees and Krull.$g8.5.$tThe Vanishing Theorem for Quasi-coherent Sheaves.$g8.6.$tCohomological Characterization of Affine Varieties.$g8.7.$tMorphisms - Direct and Inverse Image.$g8.8.$tAn Open Mapping Theorem --$gCh. 9.$tCoherent Analytic Sheaves.$g9.1.$tCoherence in the Analytic Case.$g9.2.$tOka's Theorem.$g9.3.$tIdeal Sheaves.$g9.4.$tCoherent Sheaves on Varieties.$g9.5.$tMorphisms between Coherent Sheaves.$g9.6.$tDirect and Inverse Image --$gCh. 10.$tStein Spaces.$g10.1.$tDolbeault Cohomology.$g10.2.$tChains of Syzygies.$g10.3.$tFunctional Analysis Preliminaries.$g10.4.$tCartan's Factorization Lemma.$g10.5.$tAmalgamation of Syzygies.$g10.6.$tStein Spaces --$gCh. 11.$tFrechet Sheaves - Cartan's Theorems.$g11.1.$tTopological Vector Spaces.$g11.2.$tThe Topology of H(X).$g11.3.$tFrechet Sheaves.$g11.4.$tCartan's Theorems.$g11.5.$tApplications of Cartan's Theorems.$g11.6.$tInvertible Groups and Line Bundles.
505 80 $g11.7.$tMeromorphic Functions.$g11.8.$tHolomorphic Functional Calculus.$g11.9.$tLocalization.$g11.10.$tCoherent Sheaves on Compact Varieties.$g11.11.$tSchwartz's Theorem --$gCh. 12.$tProjective Varieties.$g12.1.$tComplex Projective Space.$g12.2.$tProjective Space as an Algebraic and a Holomorphic Variety.$g12.3.$tThe Sheaves O(k) and H(k).$g12.4.$tApplications of the Sheaves O(k).$g12.5.$tEmbeddings in Projective Space --$gCh. 13.$tAlgebraic vs. Analytic - Serre's Theorems.$g13.1.$tFaithfully Flat Ring Extensions.$g13.2.$tCompletion of Local Rings.$g13.3.$tLocal Rings of Algebraic vs. Holomorphic Functions.$g13.4.$tThe Algebraic to Holomorphic Functor.$g13.5.$tSerre's Theorems.$g13.6.$tApplications --$gCh. 14.$tLie Groups and Their Representations.$g14.1.$tTopological Groups.$g14.2.$tCompact Topological Groups.$g14.3.$tLie Groups and Lie Algebras.$g14.4.$tLie Algebras.$g14.5.$tStructure of Semisimple Lie Algebras.
505 80 $g14.6.$tRepresentations of [actual symbol not reproducible][subscript 2]([Complex number system]).$g14.7.$tRepresentations of Semisimple Lie Algebras.$g14.8.$tCompact Semisimple Groups --$gCh. 15.$tAlgebraic Groups.$g15.1.$tAlgebraic Groups and Their Representations.$g15.2.$tQuotients and Group Actions.$g15.3.$tExistence of the Quotient.$g15.4.$tJordan Decomposition.$g15.5.$tTori.$g15.6.$tSolvable Algebraic Groups.$g15.7.$tSemisimple Groups and Borel Subgroups.$g15.8.$tComplex Semisimple Lie Groups --$gCh. 16.$tThe Borel-Weil-Bott Theorem.$g16.1.$tVector Bundles and Induced Representations.$g16.2.$tEquivariant Line Bundles on the Flag Variety.$g16.3.$tThe Casimir Operator.$g16.4.$tThe Borel-Weil Theorem.$g16.5.$tThe Borel-Weil-Bott Theorem.$g16.6.$tConsequences for Real Semisimple Lie Groups.$g16.7.$tInfinite Dimensional Representations.
650 0 $aFunctions of several complex variables.$0http://id.loc.gov/authorities/subjects/sh85052358
650 0 $aGeometry, Algebraic.$0http://id.loc.gov/authorities/subjects/sh85054140
830 0 $aGraduate studies in mathematics ;$vv. 46.$0http://id.loc.gov/authorities/names/n92111274
852 00 $bmat$hQA331.7$i.T39 2002g