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Several complex variables and analytic spaces   [xref: 46G20, 58B12, 58C10]
{For infinite-dimensional holomorphy, see 46G20, 58B12}
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 (must also be assigned at least one classification number from Section 01)
32-04 Explicit machine computation and programs (not the theory of computation or programming)
32-06 Proceedings, conferences, collections, etc.
32Axx Holomorphic functions of several complex variables
32A05 Power series, series of functions
32A07 Special domains (Reinhardt, Hartogs, circular, tube)
32A10 Holomorphic functions   [xref: 37F10]
32A12 Multifunctions
32A15 Entire functions
32A17 Special families of functions
32A18 Bloch functions, normal functions
32A19 Normal families of functions, mappings
32A20 Meromorphic functions   [xref: 37F10]
32A22 Nevanlinna theory (local); growth estimates; other inequalities {For geometric theory, see 32H25, 32H30}
32A25 Integral representations; canonical kernels (Szegö, Bergman, etc.)   [xref: 46F15]
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 (should also be assigned at least one classification number from Section 30) {For functions of several hypercomplex variables, see 30G35}
32A35 ${H}^p$-spaces, Nevanlinna spaces [See also 32M15, 42B30, 43A85, 46J15]   [xref: 46J15]
32A36 Bergman spaces
32A37 Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA) [See also 46Exx]   [xref: 46J15]
32A38 Algebras of holomorphic functions [See also 30H05, 46J10, 46J15]   [xref: 30H05, 46Exx, 46J15]
32A40 Boundary behavior of holomorphic functions   [xref: 46F20]
32A45 Hyperfunctions [See also 46F15]   [xref: 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
32Bxx Local analytic geometry [See also 13-XX and 14-XX]
32B05 Analytic algebras and generalizations, preparation theorems   [xref: 13J07, 26E05]
32B10 Germs of analytic sets, local parametrization
32B15 Analytic subsets of affine space
32B20 Semi-analytic sets and subanalytic sets [See also 14P15]   [xref: 14P15]
32B25 Triangulation and related questions
32B99 None of the above, but in this section
32Cxx Analytic spaces   [xref: 46M20, 53B35, 53C55, 53C56, 58Axx]
32C05 Real-analytic manifolds, real-analytic spaces [See also 14Pxx, 58A07]   [xref: 14P15, 26E05]
32C07 Real-analytic sets, complex Nash functions [See also 14P15, 14P20]   [xref: 14P20, 58A07]
32C09 Embedding of real analytic manifolds
32C11 Complex supergeometry [See also 14A22, 14M30, 58A50]   [xref: 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}   [xref: 32A27, 49Q15, 58A25]
32C35 Analytic sheaves and cohomology groups [See also 14Fxx, 18F20, 55N30]   [xref: 14F40, 18F20, 46F15, 55N30]
32C36 Local cohomology of analytic spaces   [xref: 14B15]
32C37 Duality theorems
32C38 Sheaves of differential operators and their modules, $D$-modules [See also 14F10, 16S32, 35A27, 58J15]   [xref: 13N10, 14F10, 16S32, 35A27, 35S35]
32C55 The Levi problem in complex spaces; generalizations
32C81 Applications to physics
32C99 None of the above, but in this section
32Dxx Analytic continuation
32D05 Domains of holomorphy
32D10 Envelopes of holomorphy
32D15 Continuation of analytic objects
32D20 Removable singularities
32D25 Riemann domains
32D99 None of the above, but in this section
32Exx Holomorphic convexity
32E05 Holomorphically convex complex spaces, reduction theory
32E10 Stein spaces, Stein manifolds Holomorphically convex complex spaces, reduction theory
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
32Fxx Geometric convexity
32F10 $q$-convexity, $q$-concavity   [xref: 32L15]
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
32Gxx Deformations of analytic structures   [xref: 13D10, 14D15, 14H15, 30F35, 58H15]
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]   [xref: 14J15]
32G15 Moduli of Riemann surfaces, Teichmüller theory [See also 14H15, 30Fxx]   [xref: 30F10, 30F60]
32G20 Period matrices, variation of Hodge structure; degenerations [See also 14D05, 14D07, 14K30]   [xref: 14C30, 14C34, 14D07, 14H40, 14H42, 14K30]
32G34 Moduli and deformations for ordinary differential equations (e.g. Khnizhnik-Zamolodchikov equation) [See also 34Mxx]   [xref: 34Mxx]
32G81 Applications to physics
32G99 None of the above, but in this section
32Hxx Holomorphic mappings and correspondences   [xref: 37Fxx]
32H02 Holomorphic mappings, (holomorphic) embeddings and related questions   [xref: 37F10]
32H04 Meromorphic mappings   [xref: 37F10]
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
32H99 None of the above, but in this section
32Jxx Compact analytic spaces {For Riemann surfaces, see 14Hxx, 30Fxx; for algebraic theory, see 14Jxx}   [xref: 57N13]
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]   [xref: 14C30, 58A14]
32J27 Compact Kähler manifolds: generalizations, classification
32J81 Applications to physics
32J99 None of the above, but in this section
32Kxx 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
32Lxx Holomorphic fiber spaces [See also 55Rxx]   [xref: 14F05, 14J60, 46M20, 55Rxx]
32L05 Holomorphic bundles and generalizations
32L10 Sheaves and cohomology of sections of holomorphic vector bundles, general results [See also 14F05, 18F20, 55N30]   [xref: 14F40, 18F20, 55N30]
32L15 Bundle convexity [See also 32F10]
32L20 Vanishing theorems   [xref: 14F17]
32L25 Twistor theory, double fibrations [See also 53C28]   [xref: 53C28, 81R25]
32L81 Applications to physics
32L99 None of the above, but in this section
32Mxx Complex spaces with a group of automorphisms
32M05 Complex Lie groups, automorphism groups acting on complex spaces [See also 22E10]   [xref: 22E10]
32M10 Homogeneous complex manifolds [See also 14M17, 57T15]   [xref: 14M15, 14M17, 53C30]
32M12 Almost homogeneous manifolds and spaces [See also 14M17]
32M15 Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras [See also 22E10, 22E40, 53C35, 57T15]   [xref: 32A35, 53C35]
32M17 Automorphism groups of ${\bf C}^n$ and affine manifolds
32M25 Complex vector fields   [xref: 37F75]
32M99 None of the above, but in this section
32Nxx Automorphic functions [See also 11Fxx, 20H10, 22E40, 30F35]   [xref: 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)   [xref: 12J25, 46S10, 12J27]
32Qxx Complex manifolds
32Q05 Negative curvature manifolds
32Q10 Positive curvature manifolds
32Q15 Kähler manifolds
32Q20 Kähler-Einstein manifolds [See also 53Cxx]   [xref: 53C07]
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
32Rxx   Complex dynamics ???
  • 32R05   Local dynamics around a fixed point
  • 32R10   Bifurcation theory
  • 32R15   Iterations of polynomial automorphism
  • 32R20   Dynamics of holomorphic and meromorphic maps
  • 32R25   Hyperbolic maps
  • 32R30   Classification of Fatou components
  • 32R35   Invariant currents and measures, ergodic theory
  • 32R40   Holomorphic vector fields
  • 32R45   Holomorphic foliations and laminations
  • 32R80   Computer graphs
  • 02R99   None of the above, but in this section
    32Sxx Singularities [See also 58Kxx]   [xref: 14B05, 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]   [xref: 14E15]
    32S22 Relations with arrangements of hyperplanes [See also 52C30]   [xref: 52C30]
    32S25 Surface and hypersurface singularities [See also 14J17]
    32S30 Deformations of singularities; vanishing cycles [See also 14B07]   [xref: 14B07]
    32S35 Mixed Hodge theory of singular varieties [See also 14C30, 14D07]   [xref: 14C30, 58A14]
    32S40 Monodromy; relations with differential equations and $D$-modules   [xref: 35S35, 81Q30]
    32S45 Modifications; resolution of singularities [See also 14E15]   [xref: 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]   [xref: 35S35, 58A35]
    32S65 Singularities of holomorphic vector fields and foliations   [xref: 37F75]
    32S70 Other operations on singularities
    32S99 None of the above, but in this section
    32Txx 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
    32Uxx Pluripotential theory
    32U05 Plurisubharmonic functions and generalizations [See also 31C10]   [xref: 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
    32Vxx 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
    32Wxx Differential operators in several variables [See also 32Wxx]   [xref: 32Wxx, 58Jxx]
    32W05 $\overline\partial$ and $\overline\partial$-Neumann operators   [xref: 35N15]
    32W10 $\overline\partial_b$ and $\overline\partial_b$-Neumann operators   [xref: 35N15]
    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

    Version 2000