| 14-XX | | Prev: 13 | Up: Top | Next: 15 | |
| Algebraic geometry [xref: 11Fxx, 11Gxx, 11R58, 32Bxx, 51H30] |
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 (must also be assigned at least one classification number from Section 01)
| 14-04 |
Explicit machine computation and programs (not the theory of computation or programming)
| 14-06 |
Proceedings, conferences, collections, etc.
| |
14Axx |
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
[xref: 32C11, 58A50]
| 14A25 |
Elementary questions
| 14A99 |
None of the above, but in this section
| |
14Bxx |
Local theory
| 14B05 |
Singularities [See also 14E15, 14H20, 14J17, 32Sxx, 58Kxx]
[xref: 14E15, 14H20, 14J17]
| 14B07 |
Deformations of singularities [See also 14D15, 32S30]
[xref: 14D15, 32S30]
| 14B10 |
Infinitesimal methods [See also 13D10]
[xref: 13D10]
| 14B12 |
Local deformation theory, Artin approximation, etc. [See also 13B40, 13D10]
[xref: 13B40, 13D10]
| 14B15 |
Local cohomology [See also 13D45, 32C36]
[xref: 13D45]
| 14B20 |
Formal neighborhoods
| 14B25 |
Local structure of morphisms: étale, flat, etc. [See also 13B40]
[xref: 13B40]
| 14B99 |
None of the above, but in this section
| |
14Cxx |
Cycles and subschemes
[xref: 18F25]
| 14C05 |
Parametrization (Chow and Hilbert schemes)
| 14C15 |
Chow groups and rings
| 14C17 |
Intersection theory, characteristic classes, intersection multiplicities [See also 13H15]
[xref: 13H15]
| 14C20 |
Divisors, linear systems, invertible sheaves
| 14C21 |
Pencils, nets, webs [See also 53A60]
[xref: 53A60]
| 14C22 |
Picard groups
| 14C25 |
Algebraic cycles
[xref: 19E15]
| 14C30 |
Transcendental methods, Hodge theory [See also 14D07, 32G20, 32J25, 32S35], Hodge conjecture
[xref: 14F40, 32J25, 32S35, 58A14]
| 14C34 |
Torelli problem [See also 32G20]
| 14C35 |
Applications of methods of algebraic $K$-theory [See also 19Exx]
[xref: 11G45, 13D15, 19E08, 19E15]
| 14C40 |
Riemann-Roch theorems [See also 19E20, 19L10]
| 14C99 |
None of the above, but in this section
| |
14Dxx |
Families, fibrations
| 14D05 |
Structure of families (Picard-Lefschetz, monodromy, etc.)
[xref: 32G20, 81Q30]
| 14D06 |
Fibrations, degenerations
[xref: 14R25]
| 14D07 |
Variation of Hodge structures [See also 32G20]
[xref: 14C30, 32G20, 32S35]
| 14D10 |
Arithmetic ground fields (finite, local, global)
| 14D15 |
Formal methods; deformations [See also 13D10, 14B07, 32Gxx]
[xref: 13D10, 14B07, 16S80]
| 14D20 |
Algebraic moduli problems, moduli of vector bundles {For analytic moduli problems, see 32G13}
[xref: 14H60, 14J60]
| 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
| |
14Exx |
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]
[xref: 14B05, 14J17, 32S15, 32S20, 32S45]
| 14E20 |
Coverings [See also 14H30]
[xref: 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
| |
14Fxx |
(Co)homology theory [See also 13Dxx]
[xref: 19E20, 32C35, 58A12, 58A14]
| 14F05 |
Vector bundles, sheaves, related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20]
[xref: 14H60, 14J60, 18F20, 32L10, 46M20]
| 14F10 |
Differentials and other special sheaves [See also 13Nxx, 32C38]
[xref: 13Nxx, 32C38]
| 14F17 |
Vanishing theorems [See also 32L20]
| 14F20 |
Étale and other Grothendieck topologies and cohomologies
[xref: 18F10, 19F27]
| 14F22 |
Brauer groups of schemes [See also 12G05, 16K50]
[xref: 12G05, 16K50]
| 14F25 |
Classical real and complex cohomology
| 14F30 |
$p$-adic cohomology, crystalline cohomology
| 14F35 |
Homotopy theory; fundamental groups [See also 14H30]
[xref: 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
| |
14Gxx |
Arithmetic problems. Diophantine geometry [See also 11Dxx, 11Gxx]
[xref: 11Dxx, 11Fxx, 11Gxx, 14H25, 14J20, 14K15]
| 14G05 |
Rational points
| 14G10 |
Zeta-functions and related questions [See also 11G40] (Birch-Swinnerton-Dyer conjecture)
[xref: 11G40, 19F27]
| 14G15 |
Finite ground fields
[xref: 11G25]
| 14G20 |
Local ground fields
[xref: 11F33, 11F85, 11G07, 11G25, 12H25]
| 14G22 |
Rigid analytic geometry
| 14G25 |
Global ground fields
[xref: 11G35]
| 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]
[xref: 11G18]
| 14G40 |
Arithmetic varieties and schemes; Arakelov theory; heights [See also 11G50]
[xref: 11G50]
| 14G50 |
Applications to coding theory and cryptography [See also 94A60, 94B27, 94B40]
[xref: 94A60, 94B27, 94B40]
| 14G99 |
None of the above, but in this section
| |
14Hxx |
Curves
| 14H05 |
Algebraic functions; function fields [See also 11R58]
| 14H10 |
Families, moduli (algebraic)
| 14H15 |
Families, moduli (analytic) [See also 30F10, 32Gxx]
[xref: 30F10, 32G13, 32G15]
| 14H20 |
Singularities, local rings [See also 13Hxx, 14B05]
[xref: 14B05]
| 14H25 |
Arithmetic ground fields [See also 11Dxx, 11G05, 14Gxx]
[xref: 11G20, 11G30]
| 14H30 |
Coverings, fundamental group [See also 14E20, 14F35]
[xref: 14E20, 14F35]
| 14H37 |
Automorphisms
| 14H40 |
Jacobians, Prym varieties [See also 32G20]
[xref: 14K30]
| 14H42 |
Theta functions; Schottky problem [See also 14K25, 32G20]
[xref: 14K25]
| 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]
[xref: 11G05, 11G07]
| 14H55 |
Riemann surfaces; Weierstrass points; gap sequences [See also 30Fxx]
| 14H60 |
Vector bundles on curves and their moduli [See also 14D20, 14F05]
[xref: 14F05]
| 14H70 |
Relationships with integrable systems
[xref: 37K20]
| 14H81 |
Relationships with physics
| 14H99 |
None of the above, but in this section
| |
14Jxx |
Surfaces and higher-dimensional varieties {For analytic theory, see 32Jxx}
[xref: 57N13]
| 14J10 |
Families, moduli, classification: algebraic theory
| 14J15 |
Moduli, classification: analytic theory; relations with modular forms [See also 32G13]
[xref: 32G13]
| 14J17 |
Singularities [See also 14B05, 14E15]
[xref: 14B05, 32S05, 32S25]
| 14J20 |
Arithmetic ground fields [See also 11Dxx, 11G25, 11G35, 14Gxx]
[xref: 11F41]
| 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]
[xref: 14F05]
| 14J70 |
Hypersurfaces
| 14J80 |
Topology of surfaces (Donaldson polynomials, Seiberg-Witten invariants)
| 14J81 |
Relationships with physics
| 14J99 |
None of the above, but in this section
| |
14Kxx |
Abelian varieties and schemes
[xref: 11Fxx, 11G10, 11Gxx, 14H52]
| 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]
[xref: 11G15]
| 14K25 |
Theta functions [See also 14H42]
[xref: 14H42]
| 14K30 |
Picard schemes, higher Jacobians [See also 14H40, 32G20]
[xref: 32G20]
| 14K99 |
None of the above, but in this section
| |
14Lxx |
Algebraic groups {For linear algebraic groups, see 20Gxx; for Lie algebras, see 17B45}
[xref: 11E57, 17B45]
| 14L05 |
Formal groups, $p$-divisible groups [See also 55N22]
[xref: 11G09, 11S31, 55N22]
| 14L10 |
Group varieties
| 14L15 |
Group schemes
| 14L17 |
Affine algebraic groups, hyperalgebra constructions [See also 17B45, 18D35]
| 14L24 |
Geometric invariant theory [See also 13A50]
[xref: 13A50, 14L30]
| 14L30 |
Group actions on varieties or schemes (quotients) [See also 13A50, 14L24]
[xref: 14R20]
| 14L35 |
Classical groups (geometric aspects) [See also 20Gxx, 51N30]
[xref: 51N30]
| 14L40 |
Other algebraic groups (geometric aspects)
| 14L99 |
None of the above, but in this section
| |
14Mxx |
Special varieties
| 14M05 |
Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) [See also 13F45, 13H10]
[xref: 13F15, 13H10]
| 14M06 |
Linkage [See also 13C40]
[xref: 13C40]
| 14M07 |
Low codimension problems
| 14M10 |
Complete intersections [See also 13C40]
[xref: 13C40]
| 14M12 |
Determinantal varieties [See also 13C40]
[xref: 13C40]
| 14M15 |
Grassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35]
[xref: 51M35, 53C30]
| 14M17 |
Homogeneous spaces and generalizations [See also 32M10, 53C30, 57T15]
[xref: 32M10, 32M12, 53C30]
| 14M20 |
Rational and unirational varieties
| 14M25 |
Toric varieties, Newton polyhedra [See also 52B20]
| 14M30 |
Supervarieties [See also 32C11, 58A50]
[xref: 32C11]
| 14M99 |
None of the above, but in this section
| |
14Nxx |
Projective and enumerative geometry [See also 51-XX]
[xref: 51N35]
| 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]
[xref: 53D45]
| 14N99 |
None of the above, but in this section
| |
14Pxx |
Real algebraic and real analytic geometry
[xref: 13J30, 26C15, 32C05]
| 14P05 |
Real algebraic sets [See also 12Dxx]
| 14P10 |
Semialgebraic sets and related spaces
| 14P15 |
Real analytic and semianalytic sets [See also 32B20, 32C05]
[xref: 32B20, 32C07]
| 14P20 |
Nash functions and manifolds [See also 32C07, 58A07]
[xref: 32C07, 58A07]
| 14P25 |
Topology of real algebraic varieties
| 14P99 |
None of the above, but in this section
| |
14Qxx |
Computational aspects in algebraic geometry [See also 12Y05, 13Pxx, 68W30]
[xref: 68W30]
| 14Q05 |
Curves
| 14Q10 |
Surfaces, hypersurfaces
| 14Q15 |
Higher-dimensional varieties
| 14Q20 |
Effectivity
| 14Q99 |
None of the above, but in this section
| |
14Rxx |
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
| |