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Navegando por la clasificación temática MSC 2000: 14 · Algebraic geometry
 
14 Algebraic geometry
  14-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
  14-01 Instructional exposition (textbooks, tutorial papers, etc.)
  14-02 Research exposition (monographs, survey articles)
  14-03 Historical
  14-04 Explicit machine computation and programs (not the theory of computation or programming)
  14-06 Proceedings, conferences, collections, etc.
  14-99 Algebraic geometry (not classified at a more specific level)
 
  14A Foundations
    14A05 Relevant commutative algebra [See also 13-XX]
    14A10 Varieties and morphisms
    14A15 Schemes and morphisms
    14A20 Generalizations (algebraic spaces, stacks)
    14A22 Noncommutative algebraic geometry
    14A25 Elementary questions
    14A99 None of the above, but in this section
 
  14B Local theory
    14B05 Singularities [See also 14E15, 14H20, 14J17, 32Sxx, 58Kxx]
    14B07 Deformations of singularities [See also 14D15, 32S30]
    14B10 Infinitesimal methods [See also 13D10]
    14B12 Local deformation theory, Artin approximation, etc. [See also 13B40, 13D10]
    14B15 Local cohomology [See also 13D45, 32C36]
    14B20 Formal neighborhoods
    14B25 Local structure of morphisms: étale, flat, etc. [See also 13B40]
    14B99 None of the above, but in this section
 
  14C Cycles and subschemes
    14C05 Parametrization (Chow and Hilbert schemes)
    14C15 Chow groups and rings
    14C17 Intersection theory, characteristic classes, intersection multiplicities [See also 13H15]
    14C20 Divisors, linear systems, invertible sheaves
    14C21 Pencils, nets, webs [See also 53A60]
    14C22 Picard groups
    14C25 Algebraic cycles
    14C30 Transcendental methods, Hodge theory [See also 14D07, 32G20, 32J25, 32S35]
    14C34 Torelli problem [See also 32G20]
    14C35 Applications of methods of algebraic $K$-theory [See also 19Exx]
    14C40 Riemann-Roch theorems [See also 19E20, 19L10]
    14C99 None of the above, but in this section
 
  14D Families, fibrations
    14D05 Structure of families (Picard-Lefschetz, monodromy, etc.)
    14D06 Fibrations, degenerations
    14D07 Variation of Hodge structures [See also 32G20]
    14D10 Arithmetic ground fields (finite, local, global)
    14D15 Formal methods; deformations [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)
    14D22 Fine and coarse moduli spaces
    14D99 None of the above, but in this section
 
  14E Birational geometry
    14E05 Rational and birational maps
    14E07 Birational automorphisms, Cremona group and generalizations
    14E08 Rationality questions
    14E15 Global theory and resolution of singularities [See also 14B05, 32S20, 32S45]
    14E20 Coverings [See also 14H30]
    14E22 Ramification problems [See also 11S15]
    14E25 Embeddings
    14E30 Minimal model program (Mori theory, extremal rays)
    14E99 None of the above, but in this section
 
  14F (Co)homology theory [See also 13Dxx]
    14F05 Vector bundles, sheaves, related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20]
    14F10 Differentials and other special sheaves [See also 13Nxx, 32C38]
    14F17 Vanishing theorems [See also 32L20]
    14F20 Étale and other Grothendieck topologies and cohomologies
    14F22 Brauer groups of schemes [See also 12G05, 16K50]
    14F25 Classical real and complex cohomology
    14F30 $p$-adic cohomology, crystalline cohomology
    14F35 Homotopy theory; fundamental groups [See also 14H30]
    14F40 de Rham cohomology [See also 14C30, 32C35, 32L10]
    14F42 Motivic cohomology
    14F43 Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies)
    14F45 Topological properties
    14F99 None of the above, but in this section
 
  14G Arithmetic problems. Diophantine geometry [See also 11Dxx, 11Gxx]
    14G05 Rational points
    14G10 Zeta-functions and related questions [See also 11G40]
    14G15 Finite ground fields
    14G20 Local ground fields
    14G22 Rigid analytic geometry
    14G25 Global ground fields
    14G27 Other nonalgebraically closed ground fields
    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]
    14G50 Applications to coding theory and cryptography [See also 94A60, 94B27, 94B40]
    14G99 None of the above, but in this section
 
  14H Curves
    14H05 Algebraic functions; function fields [See also 11R58]
    14H10 Families, moduli (algebraic)
    14H15 Families, moduli (analytic) [See also 30F10, 32Gxx]
    14H20 Singularities, local rings [See also 13Hxx, 14B05]
    14H25 Arithmetic ground fields [See also 11Dxx, 11G05, 14Gxx]
    14H30 Coverings, fundamental group [See also 14E20, 14F35]
    14H37 Automorphisms
    14H40 Jacobians, Prym varieties [See also 32G20]
    14H42 Theta functions; Schottky problem [See also 14K25, 32G20]
    14H45 Special curves and curves of low genus
    14H50 Plane and space curves
    14H51 Special divisors (gonality, Brill-Noether theory)
    14H52 Elliptic curves [See also 11G05, 11G07, 14Kxx]
    14H55 Riemann surfaces; Weierstrass points; gap sequences [See also 30Fxx]
    14H60 Vector bundles on curves and their moduli [See also 14D20, 14F05]
    14H70 Relationships with integrable systems
    14H81 Relationships with physics
    14H99 None of the above, but in this section
 
  14J Surfaces and higher-dimensional varieties {For analytic theory, see 32Jxx}
    14J10 Families, moduli, classification: algebraic theory
    14J15 Moduli, classification: analytic theory; relations with modular forms [See also 32G13]
    14J17 Singularities [See also 14B05, 14E15]
    14J20 Arithmetic ground fields [See also 11Dxx, 11G25, 11G35, 14Gxx]
    14J25 Special surfaces {For Hilbert modular surfaces, see 14G35}
    14J26 Rational and ruled surfaces
    14J27 Elliptic surfaces
    14J28 $K3$ surfaces and Enriques surfaces
    14J29 Surfaces of general type
    14J30 $3$-folds
    14J32 Calabi-Yau manifolds, mirror symmetry
    14J35 $4$-folds
    14J40 $n$-folds ($n>4$)
    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, 14F05, 32Lxx]
    14J70 Hypersurfaces
    14J80 Topology of surfaces (Donaldson polynomials, Seiberg-Witten invariants)
    14J81 Relationships with physics
    14J99 None of the above, but in this section
 
  14K Abelian varieties and schemes
    14K02 Isogeny
    14K05 Algebraic theory
    14K10 Algebraic moduli, classification [See also 11G15]
    14K12 Subvarieties
    14K15 Arithmetic ground fields [See also 11Dxx, 11Fxx, 11Gxx, 14Gxx]
    14K20 Analytic theory; abelian integrals and differentials
    14K22 Complex multiplication [See also 11G15]
    14K25 Theta functions [See also 14H42]
    14K30 Picard schemes, higher Jacobians [See also 14H40, 32G20]
    14K99 None of the above, but in this section
 
  14L Algebraic groups {For linear algebraic groups, see 20Gxx; for Lie algebras, see 17B45}
    14L05 Formal groups, $p$-divisible groups [See also 55N22]
    14L10 Group varieties
    14L15 Group schemes
    14L17 Affine algebraic groups, hyperalgebra constructions [See also 17B45, 18D35]
    14L24 Geometric invariant theory [See also 13A50]
    14L30 Group actions on varieties or schemes (quotients) [See also 13A50, 14L24]
    14L35 Classical groups (geometric aspects) [See also 20Gxx, 51N30]
    14L40 Other algebraic groups (geometric aspects)
    14L99 None of the above, but in this section
 
  14M Special varieties
    14M05 Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) [See also 13F45, 13H10]
    14M06 Linkage [See also 13C40]
    14M07 Low codimension problems
    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
    14M25 Toric varieties, Newton polyhedra [See also 52B20]
    14M30 Supervarieties [See also 32C11, 58A50]
    14M99 None of the above, but in this section
 
  14N Projective and enumerative geometry [See also 51-XX]
    14N05 Projective techniques [See also 51N35]
    14N10 Enumerative problems (combinatorial problems)
    14N15 Classical problems, Schubert calculus
    14N20 Configurations of linear subspaces
    14N25 Varieties of low degree
    14N30 Adjunction problems
    14N35 Gromov-Witten invariants, quantum cohomology [See also 53D45]
    14N99 None of the above, but in this section
 
  14P Real algebraic and real analytic geometry
    14P05 Real algebraic sets [See also 12Dxx]
    14P10 Semialgebraic sets and related spaces
    14P15 Real analytic and semianalytic 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
 
  14Q Computational aspects in algebraic geometry [See also 12Y05, 13Pxx, 68W30]
    14Q05 Curves
    14Q10 Surfaces, hypersurfaces
    14Q15 Higher-dimensional varieties
    14Q20 Effectivity
    14Q99 None of the above, but in this section
 
  14R Affine geometry
    14R05 Classification of affine varieties
    14R10 Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem)
    14R15 Jacobian problem
    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
 

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