14-XX
|
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 {!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
|
14A25
|
Elementary questions
|
14A99
|
None of the above, but in this section
|
14Bxx
|
Local theory
|
14B05
|
Singularities
[See also
14E15,
14H20,
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: \'etale, flat, etc.
[See also
13B40]
|
14B99
|
None of the above, but in this section
|
14Cxx
|
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],
Hodge conjecture
|
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
|
14Dxx
|
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
|
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]
|
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
|
14Fxx
|
(Co)homology theory
[See also
13Dxx]
|
14F05
|
Vector bundles, sheaves, related construction
[See also
14H60,
14J60,
18F20,
32Lxx,
46M20]
|
14F10
|
Differentials and other special sheaves
[See also
13Nxx,
32C38]
|
14F17
|
Vanishing theorems
[See also
32L20]
|
14F20
|
\'Etale 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
|
14Gxx
|
Arithmetic problems. Diophantine geometry
[See also
11Dxx,
11Gxx]
|
14G05
|
Rational points
|
14G10
|
Zeta-functions and related questions
[See also
11G40]
(Birch - Swinnerton - Dyer conjecture)
|
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)
|
14G35
|
Modular and Shimura varieties
[See also
11F41,
11F46,
11G18]
|
14G40
|
Arithmetic varieties and schemes; Arakelov theory; heights
|
14G50
|
Applications to coding theory and cryptography
[See also
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]
|
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
|
Relationship to integrable systems
|
14H81
|
Relationship to physics
|
14H99
|
None of the above, but in this section
|
14Jxx
|
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 (n4)
|
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
|
Relationship to physics
|
14J99
|
None of the above, but in this section
|
14Kxx
|
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
|
14Lxx
|
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]
|
14L25
|
Geometric invariant theory
[See also
13A50]
|
14L30
|
Group actions on varieties or schemes (quotients)
[See also
13A50,
14L25]
|
14L35
|
Classical groups (geometric aspects)
[See also
20Gxx,
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
13C14,
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
|
14Nxx
|
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
|
14Pxx
|
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
|
14Qxx
|
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
|
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
|