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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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