Mathematics Subject Classification 1991

14-XX Algebraic geometry ( 0 Dok.)

• 14-00 General reference works (handbooks, dictionaries, bibliographies, etc.) ( 0 Dok.)
• 14-01 Instructional exposition (textbooks, tutorial papers, etc.) ( 0 Dok.)
• 14-02 Research exposition (monographs, survey articles) ( 0 Dok.)
• 14-03 Historical (must be assigned at least one classification number from Section 01) ( 0 Dok.)
• 14-04 Explicit machine computation and programs (not the theory of computation or programming) ( 0 Dok.)
• 14-06 Proceedings, conferences, collections, etc. ( 0 Dok.)
• 14Axx Foundations ( 0 Dok. )
• 14A05 Relevant commutative algebra, See also {13-XX} ( 0 Dok.)
• 14A10 Varieties ( 0 Dok.)
• 14A15 Schemes ( 0 Dok.)
• 14A20 Generalizations (algebraic spaces, motifs) ( 0 Dok.)
• 14A22 Noncommutative algebraic geometry; algebraic supervarieties, See also {14M30, 32C11, 58A50} ( 0 Dok.)
• 14A25 Elementary questions ( 0 Dok.)
• 14A99 None of the above but in this section ( 0 Dok.)
• 14Bxx Local theory, See also {32Sxx} ( 0 Dok. )
• 14B05 Singularities, See also {14E15, 14H20, 32Sxx, 58C27} ( 0 Dok.)
• 14B07 Deformations of singularities, See also {14D15, 32Sxx} ( 0 Dok.)
• 14B10 Infinitesimal methods, See also {13D10} ( 0 Dok.)
• 14B12 Local deformation theory, Artin approximation, etc., See also {13B40, 13D10} ( 0 Dok.)
• 14B15 Local cohomology, See also {13D45, 32C36} ( 0 Dok.)
• 14B20 Formal neighborhoods ( 0 Dok.)
• 14B99 None of the above but in this section ( 0 Dok.)
• 14Cxx Cycles and subschemes ( 0 Dok. )
• 14C05 Parametrization (Chow and Hilbert schemes) ( 0 Dok.)
• 14C10 Equivalence relations ( 0 Dok.)
• 14C15 Rational equivalence rings ( 0 Dok.)
• 14C17 Intersection theory ( 0 Dok.)
• 14C20 Divisors, linear systems, invertible sheaves ( 0 Dok.)
• 14C21 Pencils, nets, webs, See also {53A60} ( 0 Dok.)
• 14C22 Picard groups ( 0 Dok.)
• 14C25 Algebraic cycles ( 0 Dok.)
• 14C30 Transcendental methods, Hodge theory, See also {14D07 32G20, 32J25, 32S35}, Hodge conjecture ( 0 Dok.)
• 14C34 Torelli problem, See also {32G20} ( 0 Dok.)
• 14C35 Applications of methods of algebraic $K$-theory, See Also {14F05, 19Exx} ( 0 Dok.)
• 14C40 Riemann-Roch theorems, See also {19E20, 19L10} ( 0 Dok.)
• 14C99 None of the above but in this section ( 0 Dok.)
• 14Dxx Families, fibrations ( 0 Dok. )
• 14D05 Structure of families (Picard-Lefschetz, Picard-Fuchs theory, etc.) ( 0 Dok.)
• 14D07 Variation of Hodge structures ( 0 Dok.)
• 14D10 Arithmetic ground fields (finite, local, global) ( 0 Dok.)
• 14D15 Formal methods; deformations, See also {13D10, 14B07, 16S80 32Gxx} ( 0 Dok.)
• 14D20 Algebraic moduli problems, moduli of vector bundles, {For analytic moduli problems, See 32G13} ( 0 Dok.)
• 14D22 Fine and coarse moduli spaces ( 0 Dok.)
• 14D25 Geometric invariants, See also {14L30} ( 0 Dok.)
• 14D99 None of the above but in this section ( 0 Dok.)
• 14Exx Mappings and correspondences ( 0 Dok. )
• 14E05 Rational maps, birational correspondences ( 0 Dok.)
• 14E07 Birational automorphisms, Cremona group and generalizations, See also {32G20} ( 0 Dok.)
• 14E09 Automorphisms, See also {14J50, 14L27} ( 0 Dok.)
• 14E10 General correspondences ( 0 Dok.)
• 14E15 Global theory of singularities, resolution, See Also {14B05, 32S20, 32S45} ( 0 Dok.)
• 14E20 Coverings, fundamental group (mappings) ( 0 Dok.)
• 14E22 Ramification problems, See also {11S15} ( 0 Dok.)
• 14E25 Imbeddings ( 0 Dok.)
• 14E30 Minimal models ( 0 Dok.)
• 14E35 Results in dimension $leq 3$ ( 0 Dok.)
• 14E40 Local structure of maps: etale, flat, etc., See Also { 13-XX, 14F20} ( 0 Dok.)
• 14E99 None of the above but in this section ( 0 Dok.)
• 14Fxx (Co)homology theory, See also {13Dxx} ( 0 Dok. )
• 14F05 Vector bundles, sheaves, related construction, See Also { 18F20, 32Lxx, 46M20} ( 0 Dok.)
• 14F10 Differentials and other special sheaves, See also {32C38} ( 0 Dok.)
• 14F17 Vanishing theorems, See also {32L20} ( 0 Dok.)
• 14F20 Etale and other Grothendieck topologies and cohomologies ( 0 Dok.)
• 14F25 Classical real and complex cohomology ( 0 Dok.)
• 14F30 $p$-adic cohomology, crystalline cohomology ( 0 Dok.)
• 14F32 Intersection (co)homology, See also {32S60} ( 0 Dok.)
• 14F35 Homotopy theory; fundamental groups, See also {14E20, 14H30} ( 0 Dok.)
• 14F40 de Rham cohomology, See also {14C30, 32C35, 32L10} ( 0 Dok.)
• 14F45 Topological properties ( 0 Dok.)
• 14F99 None of the above but in this section ( 0 Dok.)
• 14Gxx Arithmetic problems. Diophantine geometry, See also {11Dxx, 11Gxx} ( 0 Dok. )
• 14G05 Rationality questions, rational points ( 0 Dok.)
• 14G10 Zeta-functions and related questions, See also {11G40} (Birch-Swinnerton-Dyer conjecture) ( 0 Dok.)
• 14G15 Finite ground fields ( 0 Dok.)
• 14G20 $p$-adic ground fields ( 0 Dok.)
• 14G25 Global ground fields ( 0 Dok.)
• 14G27 Nonalgebraically closed ground fields ( 0 Dok.)
• 14G35 Modular and Shimura varieties, See also {11F41, 11F46, 11G18} ( 0 Dok.)
• 14G40 Arithmetic varieties and schemes; Arakelov theory ( 0 Dok.)
• 14G99 None of the above but in this section ( 0 Dok.)
• 14Hxx Curves ( 0 Dok. )
• 14H05 Algebraic functions; function fields, See also {11R58} ( 0 Dok.)
• 14H10 Families, moduli (algebraic) ( 0 Dok.)
• 14H15 Families, moduli (analytic), See also {30F10, 32Gxx} ( 0 Dok.)
• 14H20 Singularities, local rings, See also {13Hxx} ( 0 Dok.)
• 14H25 Arithmetic ground fields, See also {11Dxx, 11G05, 14Gxx} ( 0 Dok.)
• 14H30 Coverings, fundamental group, See also {14E20, 14F35} ( 0 Dok.)
• 14H35 Correspondences, See also {14Exx} ( 0 Dok.)
• 14H40 Jacobians, See also {32G20} ( 0 Dok.)
• 14H42 Theta functions; Schottky problem, See also {14K25, 32G20} ( 0 Dok.)
• 14H45 Special curves and curves of low genus ( 0 Dok.)
• 14H50 Space curves ( 0 Dok.)
• 14H52 Elliptic curves, See also {11G05, 11G07, 14Kxx} ( 0 Dok.)
• 14H55 Riemann surfaces; Weierstrass points; gap sequences, See also {30Fxx} ( 0 Dok.)
• 14H60 Vector bundles on curves, See also {14F05} ( 0 Dok.)
• 14H99 None of the above but in this section ( 0 Dok.)
• 14Jxx Surfaces and higher-dimensional varieties, {For analytic theory, See 32Jxx} ( 0 Dok. )
• 14J05 Picard group, See also {14C22, 19A49, 32L05} ( 0 Dok.)
• 14J10 Families, moduli, classification: algebraic theory ( 0 Dok.)
• 14J15 Moduli, classification: analytic theory, See also {32G13, 32J15} ( 0 Dok.)
• 14J17 Singularities of surfaces ( 0 Dok.)
• 14J20 Arithmetic ground fields, See also {11Dxx, 11G25, 11G35, 14Gxx} ( 0 Dok.)
• 14J25 Special surfaces, {For Hilbert modular surfaces, See 14G35} ( 0 Dok.)
• 14J26 Rational and ruled surfaces ( 0 Dok.)
• 14J27 Elliptic surfaces ( 0 Dok.)
• 14J28 $K3$ surfaces and Enriques surfaces ( 0 Dok.)
• 14J29 Surfaces of general type ( 0 Dok.)
• 14J30 Special $3$-folds, See also {14E05} ( 0 Dok.)
• 14J35 Special $4$-folds, See also {14E05} ( 0 Dok.)
• 14J40 Special $n$-folds ( 0 Dok.)
• 14J45 Fano varieties ( 0 Dok.)
• 14J50 Automorphisms of surfaces and higher-dimensional varieties, See also {14E09} ( 0 Dok.)
• 14J60 Vector bundles on surfaces and higher-dimensional varieties, See also {14F05, 32Lxx} ( 0 Dok.)
• 14J70 Hypersurfaces ( 0 Dok.)
• 14J99 None of the above but in this section ( 0 Dok.)
• 14Kxx Abelian varieties and schemes ( 0 Dok. )
• 14K02 Isogeny ( 0 Dok.)
• 14K05 Algebraic theory ( 0 Dok.)
• 14K10 Algebraic moduli, classification ( 0 Dok.)
• 14K15 Arithmetic ground fields, See also {11Dxx, 11Fxx, 11Gxx, 14Gxx} ( 0 Dok.)
• 14K20 Analytic theory; abelian integrals and differentials ( 0 Dok.)
• 14K22 Complex multiplication, See also {11G15} ( 0 Dok.)
• 14K25 Theta functions ( 0 Dok.)
• 14K30 Picard schemes, higher Jacobians, See also {14H40, 32G20} ( 0 Dok.)
• 14K99 None of the above but in this section ( 0 Dok.)
• 14Lxx Group schemes, {For linear algebraic groups, See 20Gxx. For Lie algebras, See 17B45} ( 0 Dok. )
• 14L05 Formal groups, $p$-divisible groups, See also {55N22} ( 0 Dok.)
• 14L10 Group varieties ( 0 Dok.)
• 14L15 Group schemes ( 0 Dok.)
• 14L17 Affine algebraic groups, hyperalgebra constructions, See also {17B45, 18D35} ( 0 Dok.)
• 14L27 Automorphism groups, See also {14E09} ( 0 Dok.)
• 14L30 Group actions on varieties or schemes (quotients), See also {14D25} ( 0 Dok.)
• 14L35 Classical groups (geometric aspects), See also {20Gxx, 51N30} ( 0 Dok.)
• 14L40 Other algebraic groups (geometric aspects) ( 0 Dok.)
• 14L99 None of the above but in this section ( 0 Dok.)
• 14Mxx Special varieties ( 0 Dok. )
• 14M05 Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), See also {13C14, 13F45, 13H10} ( 0 Dok.)
• 14M06 Linkage, See also {13C40} ( 0 Dok.)
• 14M07 Low codimension problems, See also {14Cxx} ( 0 Dok.)
• 14M10 Complete intersections, See also {13C40} ( 0 Dok.)
• 14M12 Determinantal varieties, See also {13C40} ( 0 Dok.)
• 14M15 Grassmannians, Schubert varieties, flag manifolds, See also {32M10, 51M35} ( 0 Dok.)
• 14M17 Homogeneous spaces and generalizations, See also {32M10, 53C30, 57T15} ( 0 Dok.)
• 14M20 Rational varieties ( 0 Dok.)
• 14M25 Toric varieties, Newton polyhedra ( 0 Dok.)
• 14M30 Supervarieties, See also {14A22, 32C11, 58A50} ( 0 Dok.)
• 14M99 None of the above but in this section ( 0 Dok.)
• 14Nxx Classical methods and problems, See also {51-XX} ( 0 Dok. )
• 14N05 Projective techniques, See also {51N35} ( 0 Dok.)
• 14N10 Enumerative problems (combinatorial problems) ( 0 Dok.)
• 14N99 None of the above but in this section ( 0 Dok.)
• 14Pxx Real algebraic and real analytic geometry ( 0 Dok. )
• 14P05 Real algebraic sets, See also {12Dxx} ( 0 Dok.)
• 14P10 Semialgebraic sets and related spaces ( 0 Dok.)
• 14P15 Real analytic and semianalytic sets, See also {32B20, 32C05} ( 0 Dok.)
• 14P20 Nash functions and manifolds, See also {32C07, 58A07} ( 0 Dok.)
• 14P25 Topology of real algebraic varieties ( 0 Dok.)
• 14P99 None of the above but in this section ( 0 Dok.)
• 14Qxx Computational aspects in algebraic geometry, See also {12-04, 68Q40} ( 0 Dok. )
• 14Q05 Curves ( 0 Dok.)
• 14Q10 Surfaces, hypersurfaces ( 0 Dok.)
• 14Q15 Higher-dimensional varieties ( 0 Dok.)
• 14Q20 Effectivity ( 0 Dok.)
• 14Q99 None of the above but in this section ( 0 Dok.)