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< 31-XX | Up | 33-XX >
32-XX Several complex variables and analytic spaces {For infinite-\newline dimensional holomorphy, see also 46G20, 58B12}
32-00   General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to several complex variables and analytic spaces
32-01   Introductory exposition (textbooks, tutorial papers, etc.) pertaining to several complex variables and analytic spaces
32-02   Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces
32-03   History of several complex variables and analytic spaces [Consider also classification numbers from Section 01-XX]
32-04   Software, source code, etc. for problems pertaining to several complex variables and analytic spaces
32-06   Proceedings, conferences, collections, etc. pertaining to several complex variables and analytic spaces
32-08   Computational methods for problems pertaining to several complex variables and analytic spaces [See also 65Exx]
32-11   Research data for problems pertaining to several complex variables and analytic spaces
32A05   Power series, series of functions of several complex variables
32A08   Polynomials and rational functions of several complex variables
32A10   Holomorphic functions of several complex variables
32A12   Multifunctions of several complex variables
32A15   Entire functions of several complex variables
32A17   Special families of functions of several complex variables
32A18   Bloch functions, normal functions of several complex variables
32A19   Normal families of holomorphic functions, mappings of several complex variables, and related topics (taut manifolds etc.)
32A20   Meromorphic functions of several complex variables
32A22   Nevanlinna theory; growth estimates; other inequalities of several complex variables {For geometric theory, see 32H25, 32H30}
32A25   Integral representations; canonical kernels (Szegő, Bergman, etc.)
32A26   Integral representations, constructed kernels (e.g., Cauchy, Fantappiè-type kernels)
32A27   Residues for several complex variables [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-XX] {For functions of several hypercomplex variables, see 30G35}
32A35   $H^p$-spaces, Nevanlinna spaces of functions in several complex variables [See also 32M15, 42B30, 43A85, 46J15]
32A36   Bergman spaces of functions in several complex variables
32A37   Other spaces of holomorphic functions of several complex variables (e.g., bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) [See also 46Exx]
32A38   Algebras of holomorphic functions of several complex variables [See also 46J10, 46J15]
32A40   Boundary behavior of holomorphic functions of several complex variables
32A45   Hyperfunctions [See also 46F15]
32A50   Harmonic analysis of several complex variables [See mainly 43-XX]
32A55   Singular integrals of functions in several complex variables
32A60   Zero sets of holomorphic functions of several complex variables
32A65   Banach algebra techniques applied to functions of several complex variables [See also 46Jxx]
32A70   Functional analysis techniques applied to functions of several complex variables [See also 46Exx]
32A99   None of the above, but in this section
32B05   Analytic algebras and generalizations, preparation theorems
32B10   Germs of analytic sets, local parametrization
32B15   Analytic subsets of affine space
32B20   Semi-analytic sets, subanalytic sets, and generalizations [See also 14P15]
32B25   Triangulation and topological properties of semi-analytic andsubanalytic sets, and related questions
32B99   None of the above, but in this section
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 [See also 32A25, 32A27]
32C35   Analytic sheaves and cohomology groups [See also 14Fxx, 18F20, 55N30]
32C36   Local cohomology of analytic spaces
32C37   Duality theorems for analytic spaces
32C38   Sheaves of differential operators and their modules, $D$-modules [See also 13N10, 14F10, 16S32, 35A27, 35S35, 58J15]
32C55   The Levi problem in complex spaces; generalizations
32C81   Applications of analytic spaces to physics and other areas of science
32C99   None of the above, but in this section
32D05   Domains of holomorphy
32D10   Envelopes of holomorphy
32D15   Continuation of analytic objects in several complex variables
32D20   Removable singularities in several complex variables
32D26   Riemann domains
32D99   None of the above, but in this section
32E05   Holomorphically convex complex spaces, reduction theory
32E10   Stein spaces
32E20   Polynomial convexity, rational convexity, meromorphic convexity in several complex variables
32E30   Holomorphic, polynomial and rational approximation, and interpolation in several complex variables; Runge pairs
32E35   Global boundary behavior of holomorphic functions of several complex variables
32E40   The Levi problem
32E99   None of the above, but in this section
32F10   $q$-convexity, $q$-concavity
32F17   Other notions of convexity in relation to several complex variables
32F18   Finite-type conditions for the boundary of a domain
32F27   Topological consequences of geometric convexity
32F32   Analytical consequences of geometric convexity (vanishing theorems, etc.)
32F45   Invariant metrics and pseudodistances in several complex variables
32F99   None of the above, but in this section
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   Complex-analytic moduli problems {For algebraic moduli problems, see 14D20, 14D22, 14H10, 14J10} [See also 14H15, 14J15]
32G15   Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) [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., Knizhnik-Zamolodchikov equation) [See also 34Mxx]
32G81   Applications of deformations of analytic structures to the sciences
32G99   None of the above, but in this section
32H02   Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables
32H04   Meromorphic mappings in several complex variables
32H12   Boundary uniqueness of mappings in several complex variables
32H25   Picard-type theorems and generalizations for several complex variables {For function-theoretic properties, see 32A22}
32H30   Value distribution theory in higher dimensions {For function-theoretic properties, see 32A22}
32H35   Proper holomorphic mappings, finiteness theorems
32H40   Boundary regularity of mappings in several complex variables
32H50   Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables
32H99   None of the above, but in this section
32J05   Compactification of analytic spaces
32J10   Algebraic dependence theorems
32J15   Compact complex surfaces
32J17   Compact complex $3$-folds
32J18   Compact complex $n$-folds
32J25   Transcendental methods of algebraic geometry (complex-analytic aspects) [See also 14C30]
32J27   Compact Kähler manifolds: generalizations, classification
32J81   Applications of compact analytic spaces to the sciences
32J99   None of the above, but in this section
32K05   Banach analytic manifolds and spaces [See also 46G20, 58Bxx]
32K07   Formal and graded complex spaces [See also 58C50]
32K12   Holomorphic maps with infinite-dimensional arguments or values [See also 46G20]
32K15   Differentiable functions on analytic spaces, differentiable spaces [See also 58C25]
32K99   None of the above, but in this section
32L05   Holomorphic bundles and generalizations
32L10   Sheaves and cohomology of sections of holomorphic vector bundles, general results [See also 14F06, 14H60, 14J60, 18F20, 55N30]
32L15   Bundle convexity [See also 32F10]
32L20   Vanishing theorems
32L25   Twistor theory, double fibrations (complex-analytic aspects) [See also 53C28]
32L81   Applications of holomorphic fiber spaces to the sciences
32L99   None of the above, but in this section
32M05   Complex Lie groups, group actions 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 (complex-analytic aspects) [See also 22E10, 22E40, 53C35, 57T15]
32M17   Automorphism groups of $\mathbb{C}^n$ and affine manifolds
32M18   Automorphism groups of other complex spaces
32M25   Complex vector fields, holomorphic foliations, $\mathbb{C}$-actions
32M99   None of the above, but in this section
32N05   General theory of automorphic functions of several complex variables
32N10   Automorphic forms in several complex variables
32N15   Automorphic functions in symmetric domains
32N99   None of the above, but in this section
32P05   Non-Archimedean analysis [Should also be assigned at least one other classification number from Section 32-XX describing the type of problem]
32P99   None of the above, but in this section
32Q02   Special domains (Reinhardt, Hartogs, circular, tube, etc.) in $\mathbb{C}^n$ and complex manifolds
32Q05   Negative curvature complex manifolds
32Q10   Positive curvature complex manifolds
32Q15   Kähler manifolds
32Q20   Kähler-Einstein manifolds [See also 53Cxx]
32Q25   Calabi-Yau theory (complex-analytic aspects) [See also 14J32]
32Q26   Notions of stability for complex manifolds
32Q28   Stein manifolds
32Q30   Uniformization of complex manifolds
32Q35   Complex manifolds as subdomains of Euclidean space
32Q40   Embedding theorems for complex manifolds
32Q45   Hyperbolic and Kobayashi hyperbolic manifolds
32Q55   Topological aspects of complex manifolds
32Q56   Oka principle and Oka manifolds
32Q57   Classification theorems for complex manifolds
32Q60   Almost complex manifolds
32Q65   Pseudoholomorphic curves
32Q99   None of the above, but in this section
32S05   Local complex singularities [See also 14J17]
32S10   Invariants of analytic local rings
32S15   Equisingularity (topological and analytic) [See also 14E15]
32S20   Global theory of complex singularities; cohomological properties [See also 14E15]
32S22   Relations with arrangements of hyperplanes [See also 52C35]
32S25   Complex surface and hypersurface singularities [See also 14J17]
32S30   Deformations of complex singularities; vanishing cycles [See also 14B07]
32S35   Mixed Hodge theory of singular varieties (complex-analytic aspects) [See also 14C30, 14D07]
32S40   Monodromy; relations with differential equations and $D$-modules (complex-analytic aspects)
32S45   Modifications; resolution of singularities (complex-analytic aspects) [See also 14E15]
32S50   Topological aspects of complex singularities: Lefschetz theorems, topological classification, invariants
32S55   Milnor fibration; relations with knot theory [See also 57K10, 57K45]
32S60   Stratifications; constructible sheaves; intersection cohomology (complex-analytic aspects) [See also 58Kxx]
32S65   Singularities of holomorphic vector fields and foliations
32S70   Other operations on complex singularities
32S99   None of the above, but in this section
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
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 in pluripotential theory
32U35   Plurisubharmonic extremal functions, pluricomplex Green functions
32U40   Currents
32U99   None of the above, but in this section
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
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 in several variables
32W99   None of the above, but in this section
< 31-XX | Up | 33-XX >
 
 
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