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Navegando por la clasificación temática MSC 2000: 32 · Several complex variables and analytic spaces
 32 Several complex variables and analytic spaces 32-00 General reference works (handbooks, dictionaries, bibliographies, etc.) 32-01 Instructional exposition (textbooks, tutorial papers, etc.) 32-02 Research exposition (monographs, survey articles) 32-03 Historical 32-04 Explicit machine computation and programs (not the theory of computation or programming) 32-06 Proceedings, conferences, collections, etc. 32-99 Several complex variables and analytic spaces (not classified at a more specific level) 32A Holomorphic functions of several complex variables 32A05 Power series, series of functions 32A07 Special domains (Reinhardt, Hartogs, circular, tube) 32A10 Holomorphic functions 32A12 Multifunctions 32A15 Entire functions 32A17 Special families of functions 32A18 Bloch functions, normal functions 32A19 Normal families of functions, mappings 32A20 Meromorphic functions 32A22 Nevanlinna theory (local); growth estimates; other inequalities {For geometric theory, see 32H25, 32H30} 32A25 Integral representations; canonical kernels (Szegö, Bergman, etc.) 32A26 Integral representations, constructed kernels (e.g. Cauchy, Fantappiè-type kernels) 32A27 Local theory of residues [See also 32C30] 32A30 Other generalizations of function theory of one complex variable {For functions of several hypercomplex variables, see 30G35} (should also be assigned at least one classification number from Section 30) 32A35 ${H}^p$-spaces, Nevanlinna spaces [See also 32M15, 42B30, 43A85, 46J15] 32A36 Bergman spaces 32A37 Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) [See also 46Exx] 32A38 Algebras of holomorphic functions [See also 30H05, 46J10, 46J15] 32A40 Boundary behavior of holomorphic functions 32A45 Hyperfunctions [See also 46F15] 32A50 Harmonic analysis of several complex variables [See mainly 43-XX] 32A55 Singular integrals 32A60 Zero sets of holomorphic functions 32A65 Banach algebra techniques [See mainly 46Jxx] 32A70 Functional analysis techniques [See mainly 46Exx] 32A99 None of the above, but in this section 32B Local analytic geometry [See also 13-XX and 14-XX] 32B05 Analytic algebras and generalizations, preparation theorems 32B10 Germs of analytic sets, local parametrization 32B15 Analytic subsets of affine space 32B20 Semi-analytic sets and subanalytic sets [See also 14P15] 32B25 Triangulation and related questions 32B99 None of the above, but in this section 32C Analytic spaces 32C05 Real-analytic manifolds, real-analytic spaces [See also 14Pxx, 58A07] 32C07 Real-analytic sets, complex Nash functions [See also 14P15, 14P20] 32C09 Embedding of real analytic manifolds 32C11 Complex supergeometry [See also 14A22, 14M30, 58A50] 32C15 Complex spaces 32C18 Topology of analytic spaces 32C20 Normal analytic spaces 32C22 Embedding of analytic spaces 32C25 Analytic subsets and submanifolds 32C30 Integration on analytic sets and spaces, currents {For local theory, see 32A25 or 32A27} 32C35 Analytic sheaves and cohomology groups [See also 14Fxx, 18F20, 55N30] 32C36 Local cohomology of analytic spaces 32C37 Duality theorems 32C38 Sheaves of differential operators and their modules, $D$-modules [See also 14F10, 16S32, 35A27, 58J15] 32C55 The Levi problem in complex spaces; generalizations 32C81 Applications to physics 32C99 None of the above, but in this section 32D Analytic continuation 32D05 Domains of holomorphy 32D10 Envelopes of holomorphy 32D15 Continuation of analytic objects 32D20 Removable singularities 32D26 Riemann domains 32D99 None of the above, but in this section 32E Holomorphic convexity 32E05 Holomorphically convex complex spaces, reduction theory 32E10 Stein spaces, Stein manifolds 32E20 Polynomial convexity 32E30 Holomorphic and polynomial approximation, Runge pairs, interpolation 32E35 Global boundary behavior of holomorphic functions 32E40 The Levi problem 32E99 None of the above, but in this section 32F Geometric convexity 32F10 $q$-convexity, $q$-concavity 32F17 Other notions of convexity 32F18 Finite-type conditions 32F27 Topological consequences of geometric convexity 32F32 Analytical consequences of geometric convexity (vanishing theorems, etc.) 32F45 Invariant metrics and pseudodistances 32F99 None of the above, but in this section 32G Deformations of analytic structures 32G05 Deformations of complex structures [See also 13D10, 16S80, 58H10, 58H15] 32G07 Deformations of special (e.g. CR) structures 32G08 Deformations of fiber bundles 32G10 Deformations of submanifolds and subspaces 32G13 Analytic moduli problems {For algebraic moduli problems, see 14D20, 14D22, 14H10, 14J10} [See also 14H15, 14J15] 32G15 Moduli of Riemann surfaces, Teichmüller theory [See also 14H15, 30Fxx] 32G20 Period matrices, variation of Hodge structure; degenerations [See also 14D05, 14D07, 14K30] 32G34 Moduli and deformations for ordinary differential equations (e.g. Khnizhnik-Zamolodchikov equation) [See also 34Mxx] 32G81 Applications to physics 32G99 None of the above, but in this section 32H Holomorphic mappings and correspondences 32H02 Holomorphic mappings, (holomorphic) embeddings and related questions 32H04 Meromorphic mappings 32H12 Boundary uniqueness of mappings 32H25 Picard-type theorems and generalizations {For function-theoretic properties, see 32A22} 32H30 Value distribution theory in higher dimensions {For function-theoretic properties, see 32A22} 32H35 Proper mappings, finiteness theorems 32H40 Boundary regularity of mappings 32H50 Iteration problems 32H99 None of the above, but in this section 32J Compact analytic spaces {For Riemann surfaces, see 14Hxx, 30Fxx; for algebraic theory, see 14Jxx} 32J05 Compactification of analytic spaces 32J10 Algebraic dependence theorems 32J15 Compact surfaces 32J17 Compact $3$-folds 32J18 Compact $n$-folds 32J25 Transcendental methods of algebraic geometry [See also 14C30] 32J27 Compact Kähler manifolds: generalizations, classification 32J81 Applications to physics 32J99 None of the above, but in this section 32K Generalizations of analytic spaces (should also be assigned at least one other classification number from Section 32 describing the type of problem) 32K05 Banach analytic spaces [See also 58Bxx] 32K07 Formal and graded complex spaces [See also 58C50] 32K15 Differentiable functions on analytic spaces, differentiable spaces [See also 58C25] 32K99 None of the above, but in this section 32L Holomorphic fiber spaces [See also 55Rxx] 32L05 Holomorphic bundles and generalizations 32L10 Sheaves and cohomology of sections of holomorphic vector bundles, general results [See also 14F05, 18F20, 55N30] 32L15 Bundle convexity [See also 32F10] 32L20 Vanishing theorems 32L25 Twistor theory, double fibrations [See also 53C28] 32L81 Applications to physics 32L99 None of the above, but in this section 32M Complex spaces with a group of automorphisms 32M05 Complex Lie groups, automorphism groups acting on complex spaces [See also 22E10] 32M10 Homogeneous complex manifolds [See also 14M17, 57T15] 32M12 Almost homogeneous manifolds and spaces [See also 14M17] 32M15 Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras [See also 22E10, 22E40, 53C35, 57T15] 32M17 Automorphism groups of ${\bf C}^n$ and affine manifolds 32M25 Complex vector fields 32M99 None of the above, but in this section 32N Automorphic functions [See also 11Fxx, 20H10, 22E40, 30F35] 32N05 General theory of automorphic functions of several complex variables 32N10 Automorphic forms 32N15 Automorphic functions in symmetric domains 32N99 None of the above, but in this section 32P05 Non-Archimedean complex analysis (should also be assigned at least one other classification number from Section 32 describing the type of problem) 32Q Complex manifolds 32Q05 Negative curvature manifolds 32Q10 Positive curvature manifolds 32Q15 Kähler manifolds 32Q20 Kähler-Einstein manifolds [See also 53Cxx] 32Q25 Calabi-Yau theory 32Q28 Stein manifolds 32Q30 Uniformization 32Q35 Complex manifolds as subdomains of Euclidean space 32Q40 Embedding theorems 32Q45 Hyperbolic and Kobayashi hyperbolic manifolds 32Q55 Topological aspects of complex manifolds 32Q57 Classification theorems 32Q60 Almost complex manifolds 32Q65 Pseudoholomorphic curves 32Q99 None of the above, but in this section 32S Singularities [See also 58Kxx] 32S05 Local singularities [See also 14J17] 32S10 Invariants of analytic local rings 32S15 Equisingularity (topological and analytic) [See also 14E15] 32S20 Global theory of singularities; cohomological properties [See also 14E15] 32S22 Relations with arrangements of hyperplanes [See also 52C35] 32S25 Surface and hypersurface singularities [See also 14J17] 32S30 Deformations of singularities; vanishing cycles [See also 14B07] 32S35 Mixed Hodge theory of singular varieties [See also 14C30, 14D07] 32S40 Monodromy; relations with differential equations and $D$-modules 32S45 Modifications; resolution of singularities [See also 14E15] 32S50 Topological aspects: Lefschetz theorems, topological classification, invariants 32S55 Milnor fibration; relations with knot theory [See also 57M25, 57Q45] 32S60 Stratifications; constructible sheaves; intersection cohomology [See also 58Kxx] 32S65 Singularities of holomorphic vector fields and foliations 32S70 Other operations on singularities 32S99 None of the above, but in this section 32T Pseudoconvex domains 32T05 Domains of holomorphy 32T15 Strongly pseudoconvex domains 32T20 Worm domains 32T25 Finite type domains 32T27 Geometric and analytic invariants on weakly pseudoconvex boundaries 32T35 Exhaustion functions 32T40 Peak functions 32T99 None of the above, but in this section 32U Pluripotential theory 32U05 Plurisubharmonic functions and generalizations [See also 31C10] 32U10 Plurisubharmonic exhaustion functions 32U15 General pluripotential theory 32U20 Capacity theory and generalizations 32U25 Lelong numbers 32U30 Removable sets 32U35 Pluricomplex Green functions 32U40 Currents 32U99 None of the above, but in this section 32V CR manifolds 32V05 CR structures, CR operators, and generalizations 32V10 CR functions 32V15 CR manifolds as boundaries of domains 32V20 Analysis on CR manifolds 32V25 Extension of functions and other analytic objects from CR manifolds 32V30 Embeddings of CR manifolds 32V35 Finite type conditions on CR manifolds 32V40 Real submanifolds in complex manifolds 32V99 None of the above, but in this section 32W Differential operators in several complex variables 32W05 $\overline\partial$ and $\overline\partial$-Neumann operators 32W10 $\overline\partial_b$ and $\overline\partial_b$-Neumann operators 32W20 Complex Monge-Ampère operators 32W25 Pseudodifferential operators in several complex variables 32W30 Heat kernels in several complex variables 32W50 Other partial differential equations of complex analysis 32W99 None of the above, but in this section

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