CZ:Mathematics Workgroup

14-XX Algebraic geometry

• 14Axx Foundations
  • 14A10 Varieties and morphisms
  • 14A15 Schemes and morphisms
  • 14A20 Generalizations (algebraic spaces, stacks)
  • 14A22 Noncommutative algebraic geometry
• 14Bxx 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 morphism, flat morphism, etc. [See also 13B40]
• 14Cxx Cycles and subschemes
  • 14C05 Parametrization (Chow schemes 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]
    • Riemann-Roch theorem
    • Clifford's theorem
    • Grothendieck Riemann-Roch theorem
• 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 moduli spaces and coarse moduli spaces
• 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)
• 14Fxx (Co)homology theory [See also 13Dxx]
  • 14F05 Vector bundles, sheaves, related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20]
  • 14F10 sheaf of Differentials and other special sheaves [See also 13Nxx, 32C38]
  • 14F17 Vanishing theorems [See also 32L20]
  • 14F20 Étale topology Etale cohomology and other Grothendieck topologies and Grothendieck 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 cohomology, equivariant cohomology, Lawson, Deligne (co)homologies)
  • 14F45 Topological properties
• 14Gxx Arithmetic problems. Diophantine geometry [See also 11Dxx, 11Gxx]
• 14Hxx Curves
  • 14H05 Algebraic functions; function fields [See also 11R58]
  • 14H10,14H15 moduli [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

hyperelliptic curve

• • 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]
• 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 of surfaces [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 surfaces and ruled surfaces
  • 14J27 Elliptic surfaces
  • 14J28 K3 surfaces and Enriques surfaces

Kummer 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)
• 14Kxx Abelian varieties and schemes
• 14Lxx Algebraic groups {For linear algebraic groups, see 20Gxx; for Lie algebras, see 17B45}
• 14Mxx Special varieties
• 14Nxx Projective and enumerative geometry [See also 51-xx]
• 14Pxx Real algebraic and real analytic geometry
• 14Qxx Computational algebraic geometry [See also 12Y05, 13Pxx, 68W30]
• 14Rxx Affine geometry