14-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to algebraic geometry 29

14-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry 494

14A30 Fundamental constructions in algebraic geometry involving higher and derived categories (homotopical algebraic geometry, derived algebraic geometry, etc.) {For categorical aspects, see 18Fxx, 18Gxx} 46

14C17 Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry [See also 13H15] 1462

14C30 Transcendental methods, Hodge theory (algebro-geometric aspects) [See also 14D07, 32G20, 32J25, 32S35, 58A14], Hodge conjecture 1836

14D20 Algebraic moduli problems, moduli of vector bundles {For analytic moduli problems, see 32G13} 2551

14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) [See also 32L25, 81Txx] 1530

14E15 Global theory and resolution of singularities (algebro-geometric aspects) [See also 14B05, 32S20, 32S45] 1646

14F08 Derived categories of sheaves, dg categories, and related constructions in algebraic geometry [See also 14A30, 14F06, 18Gxx] 399

14F10 Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials [See also 13Nxx, 32C38] 1385

14F43 Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies) 768

14G10 Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) [See also 11G40] 1573

14G32 Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory) 307

14G50 Applications to coding theory and cryptography of arithmetic geometry [See also 94A60, 94B27, 94B40] 1832

14J17 Singularities of surfaces or higher-dimensional varieties [See also 14B05, 14E15, 32S05, 32S25] 2052

14J20 Arithmetic ground fields for surfaces or higher-dimensional varieties [See also 11Dxx, 11G25, 11G35, 14Gxx] 386

14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli [See also 14D20, 14F06, 14H60, 32Lxx] 1847

14Lxx Algebraic groups [See also 11E57] {For Lie algebras, see 17B45; for linear algebraic groups, see 20Gxx} 7637

14M05 Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) [See also 13F15, 13F45, 13H10] 1284

14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) [See also 53D45] 1918

14Qxx Computational aspects in algebraic geometry {For software etc., see 14-04} [See also 12-08, 13Pxx, 68W30] 2723

14Q25 Computational algebraic geometry over arithmetic ground fields [See also 14Gxx, 14H25, 14Kxx] 2

14T10 Foundations of tropical geometry and relations with algebra {For algebraic aspects, see 15A80} 61