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< 13-XX | Up | 15-XX >
14-XX Algebraic geometry
14-00   General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to algebraic geometry
14-01   Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry
14-02   Research exposition (monographs, survey articles) pertaining to algebraic geometry
14-03   History of algebraic geometry [Consider also classification numbers from Section 01-XX]
14-04   Software, source code, etc. for problems pertaining to algebraic geometry
14-06   Proceedings, conferences, collections, etc. pertaining to algebraic geometry
14-11   Research data for problems pertaining to algebraic geometry
14A05   Relevant commutative algebra [See also 13-XX]
14A10   Varieties and morphisms
14A15   Schemes and morphisms
14A20   Generalizations (algebraic spaces, stacks)
14A21   Logarithmic algebraic geometry, log schemes
14A22   Noncommutative algebraic geometry [See also 16S38]
14A23   Geometry over the field with one element
14A25   Elementary questions in algebraic geometry
14A30   Fundamental constructions in algebraic geometry involving higher and derived categories (homotopical algebraic geometry, derived algebraic geometry, etc.) {For categorical aspects, see 18Fxx, 18Gxx}
14A99   None of the above, but in this section
14B05   Singularities in algebraic geometry [See also 14E15, 14H20, 14J17, 32Sxx, 58Kxx]
14B07   Deformations of singularities [See also 14D15, 32S30]
14B10   Infinitesimal methods in algebraic geometry [See also 13D10]
14B12   Local deformation theory, Artin approximation, etc. [See also 13B40, 13D10]
14B15   Local cohomology and algebraic geometry [See also 13D45, 32C36]
14B20   Formal neighborhoods in algebraic geometry
14B25   Local structure of morphisms in algebraic geometry: étale, flat, etc. [See also 13B40]
14B99   None of the above, but in this section
14C05   Parametrization (Chow and Hilbert schemes)
14C15   (Equivariant) Chow groups and rings; motives
14C17   Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry [See also 13H15]
14C20   Divisors, linear systems, invertible sheaves
14C21   Pencils, nets, webs in algebraic geometry [See also 53A60]
14C22   Picard groups
14C25   Algebraic cycles
14C30   Transcendental methods, Hodge theory (algebro-geometric aspects) [See also 14D07, 32G20, 32J25, 32S35, 58A14], Hodge conjecture
14C34   Torelli problem [See also 32G20]
14C35   Applications of methods of algebraic $K$-theory in algebraic geometry [See also 19Exx]
14C40   Riemann-Roch theorems [See also 19E20, 19L10]
14C99   None of the above, but in this section
14D05   Structure of families (Picard-Lefschetz, monodromy, etc.)
14D06   Fibrations, degenerations in algebraic geometry
14D07   Variation of Hodge structures (algebro-geometric aspects) [See also 32G20]
14D10   Arithmetic ground fields (finite, local, global) and families or fibrations
14D15   Formal methods and deformations in algebraic geometry [See also 13D10, 14B07, 32Gxx]
14D20   Algebraic moduli problems, moduli of vector bundles {For analytic moduli problems, see 32G13}
14D21   Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) [See also 32L25, 81Txx]
14D22   Fine and coarse moduli spaces
14D23   Stacks and moduli problems
14D24   Geometric Langlands program (algebro-geometric aspects) [See also 22E57]
14D99   None of the above, but in this section
14E05   Rational and birational maps
14E07   Birational automorphisms, Cremona group and generalizations
14E08   Rationality questions in algebraic geometry [See also 14M20]
14E15   Global theory and resolution of singularities (algebro-geometric aspects) [See also 14B05, 32S20, 32S45]
14E16   McKay correspondence
14E18   Arcs and motivic integration
14E20   Coverings in algebraic geometry [See also 14H30]
14E22   Ramification problems in algebraic geometry [See also 11S15]
14E25   Embeddings in algebraic geometry
14E30   Minimal model program (Mori theory, extremal rays)
14E99   None of the above, but in this section
14F06   Sheaves in algebraic geometry [See also 14F08, 14H60, 14J60, 18F20, 32L10, 46M20]
14F08   Derived categories of sheaves, dg categories, and related constructions in algebraic geometry [See also 14A30, 14F06, 18Gxx]
14F10   Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials [See also 13Nxx, 32C38]
14F17   Vanishing theorems in algebraic geometry [See also 32L20]
14F18   Multiplier ideals
14F20   Étale and other Grothendieck topologies and (co)homologies
14F22   Brauer groups of schemes [See also 12G05, 16K50]
14F25   Classical real and complex (co)homology in algebraic geometry
14F30   $p$-adic cohomology, crystalline cohomology
14F35   Homotopy theory and fundamental groups in algebraic geometry [See also 14H30]
14F40   de Rham cohomology and algebraic geometry [See also 14C30, 32C35, 32L10]
14F42   Motivic cohomology; motivic homotopy theory [See also 19E15]
14F43   Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies)
14F45   Topological properties in algebraic geometry
14F99   None of the above, but in this section
14G05   Rational points
14G10   Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) [See also 11G40]
14G12   Hasse principle, weak and strong approximation, Brauer-Manin obstruction [See also 14F22]
14G15   Finite ground fields in algebraic geometry
14G17   Positive characteristic ground fields in algebraic geometry
14G20   Local ground fields in algebraic geometry
14G22   Rigid analytic geometry
14G25   Global ground fields in algebraic geometry
14G27   Other nonalgebraically closed ground fields in algebraic geometry
14G32   Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory)
14G35   Modular and Shimura varieties [See also 11F41, 11F46, 11G18]
14G40   Arithmetic varieties and schemes; Arakelov theory; heights [See also 11G50, 37P30]
14G45   Perfectoid spaces and mixed characteristic
14G50   Applications to coding theory and cryptography of arithmetic geometry [See also 94A60, 94B27, 94B40]
14G99   None of the above, but in this section
14H05   Algebraic functions and function fields in algebraic geometry [See also 11R58]
14H10   Families, moduli of curves (algebraic)
14H15   Families, moduli of curves (analytic) [See also 30F10, 32G15]
14H20   Singularities of curves, local rings [See also 13Hxx, 14B05]
14H25   Arithmetic ground fields for curves [See also 11Dxx, 11G05, 14Gxx]
14H30   Coverings of curves, fundamental group [See also 14E20, 14F35]
14H37   Automorphisms of curves
14H40   Jacobians, Prym varieties [See also 32G20]
14H42   Theta functions and curves; Schottky problem [See also 14K25, 32G20]
14H45   Special algebraic curves and curves of low genus
14H50   Plane and space curves
14H51   Special divisors on curves (gonality, Brill-Noether theory)
14H52   Elliptic curves [See also 11G05, 11G07, 14Kxx]
14H55   Riemann surfaces; Weierstrass points; gap sequences [See also 30Fxx]
14H57   Dessins d'enfants theory {For arithmetic aspects, see 11G32}
14H60   Vector bundles on curves and their moduli [See also 14D20, 14F06, 14J60]
14H70   Relationships between algebraic curves and integrable systems
14H81   Relationships between algebraic curves and physics
14H99   None of the above, but in this section
14J10   Families, moduli, classification: algebraic theory
14J15   Moduli, classification: analytic theory; relations with modular forms [See also 32G13]
14J17   Singularities of surfaces or higher-dimensional varieties [See also 14B05, 14E15, 32S05, 32S25]
14J20   Arithmetic ground fields for surfaces or higher-dimensional varieties [See also 11Dxx, 11G25, 11G35, 14Gxx]
14J25   Special surfaces {For Hilbert modular surfaces, see 14G35}
14J26   Rational and ruled surfaces
14J27   Elliptic surfaces, elliptic or Calabi-Yau fibrations
14J28   $K3$ surfaces and Enriques surfaces
14J29   Surfaces of general type
14J30   $3$-folds
14J32   Calabi-Yau manifolds (algebro-geometric aspects) [See also 32Q25]
14J33   Mirror symmetry (algebro-geometric aspects) [See also 11G42, 53D37]
14J35   $4$-folds
14J40   $n$-folds ($n>4$)
14J42   Holomorphic symplectic varieties, hyper-Kähler varieties
14J45   Fano varieties
14J50   Automorphisms of surfaces and higher-dimensional varieties
14J60   Vector bundles on surfaces and higher-dimensional varieties, and their moduli [See also 14D20, 14F06, 14H60, 32Lxx]
14J70   Hypersurfaces and algebraic geometry
14J80   Topology of surfaces (Donaldson polynomials, Seiberg-Witten invariants)
14J81   Relationships between surfaces, higher-dimensional varieties, and physics
14J99   None of the above, but in this section
14K02   Isogeny
14K05   Algebraic theory of abelian varieties
14K10   Algebraic moduli of abelian varieties, classification [See also 11G15]
14K12   Subvarieties of abelian varieties
14K15   Arithmetic ground fields for abelian varieties [See also 11Dxx, 11Fxx, 11G10, 14Gxx]
14K20   Analytic theory of abelian varieties; abelian integrals and differentials
14K22   Complex multiplication and abelian varieties [See also 11G15]
14K25   Theta functions and abelian varieties [See also 14H42]
14K30   Picard schemes, higher Jacobians [See also 14H40, 32G20]
14K99   None of the above, but in this section
14L05   Formal groups, $p$-divisible groups [See also 55N22]
14L10   Group varieties
14L15   Group schemes
14L17   Affine algebraic groups, hyperalgebra constructions [See also 17B45, 18C40]
14L24   Geometric invariant theory [See also 13A50]
14L30   Group actions on varieties or schemes (quotients) [See also 13A50, 14L24, 14M17]
14L35   Classical groups (algebro-geometric aspects) [See also 20Gxx, 51N30]
14L40   Other algebraic groups (geometric aspects)
14L99   None of the above, but in this section
14M05   Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) [See also 13F15, 13F45, 13H10]
14M06   Linkage [See also 13C40]
14M07   Low codimension problems in algebraic geometry
14M10   Complete intersections [See also 13C40]
14M12   Determinantal varieties [See also 13C40]
14M15   Grassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35]
14M17   Homogeneous spaces and generalizations [See also 32M10, 53C30, 57T15]
14M20   Rational and unirational varieties [See also 14E08]
14M22   Rationally connected varieties
14M25   Toric varieties, Newton polyhedra, Okounkov bodies [See also 52B20]
14M27   Compactifications; symmetric and spherical varieties
14M30   Supervarieties [See also 32C11, 58A50]
14M35   Character varieties
14M99   None of the above, but in this section
14N05   Projective techniques in algebraic geometry [See also 51N35]
14N07   Secant varieties, tensor rank, varieties of sums of powers
14N10   Enumerative problems (combinatorial problems) in algebraic geometry
14N15   Classical problems, Schubert calculus
14N20   Configurations and arrangements of linear subspaces
14N25   Varieties of low degree
14N30   Adjunction problems
14N35   Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) [See also 53D45]
14N99   None of the above, but in this section
14P05   Real algebraic sets [See also 12D15, 13J30]
14P10   Semialgebraic sets and related spaces
14P15   Real-analytic and semi-analytic sets [See also 32B20, 32C05]
14P20   Nash functions and manifolds [See also 32C07, 58A07]
14P25   Topology of real algebraic varieties
14P99   None of the above, but in this section
14Q05   Computational aspects of algebraic curves [See also 14Hxx]
14Q10   Computational aspects of algebraic surfaces [See also 14Jxx]
14Q15   Computational aspects of higher-dimensional varieties [See also 14Jxx, 14Mxx]
14Q20   Effectivity, complexity and computational aspects of algebraic geometry
14Q25   Computational algebraic geometry over arithmetic ground fields [See also 14Gxx, 14H25, 14Kxx]
14Q30   Computational real algebraic geometry [See also 14Pxx]
14Q65   Geometric aspects of numerical algebraic geometry [See also 65H14]
14Q99   None of the above, but in this section
14R05   Classification of affine varieties
14R10   Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem)
14R15   Jacobian problem [See also 13F20]
14R20   Group actions on affine varieties [See also 13A50, 14L30]
14R25   Affine fibrations [See also 14D06]
14R99   None of the above, but in this section
14T10   Foundations of tropical geometry and relations with algebra {For algebraic aspects, see 15A80}
14T15   Combinatorial aspects of tropical varieties
14T20   Geometric aspects of tropical varieties
14T25   Arithmetic aspects of tropical varieties
14T90   Applications of tropical geometry
14T99   None of the above, but in this section
< 13-XX | Up | 15-XX >
 
 
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