Leseprobe
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Topics in Algebraic and Analytic Geometry. (MN-13), Volume 13
John Frank Adams, Phillip A. Griffiths
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Naturwissenschaften, Medizin, Informatik, Technik / Geometrie
Beschreibung
This volume offers a systematic treatment of certain basic parts of algebraic geometry, presented from the analytic and algebraic points of view. The notes focus on comparison theorems between the algebraic, analytic, and continuous categories.
Contents include: 1.1 sheaf theory, ringed spaces; 1.2 local structure of analytic and algebraic sets; 1.3 Pn 2.1 sheaves of modules; 2.2 vector bundles; 2.3 sheaf cohomology and computations on Pn; 3.1 maximum principle and Schwarz lemma on analytic spaces; 3.2 Siegel's theorem; 3.3 Chow's theorem; 4.1 GAGA; 5.1 line bundles, divisors, and maps to Pn; 5.2 Grassmanians and vector bundles; 5.3 Chern classes and curvature; 5.4 analytic cocycles; 6.1 K-theory and Bott periodicity; 6.2 K-theory as a generalized cohomology theory; 7.1 the Chern character and obstruction theory; 7.2 the Atiyah-Hirzebruch spectral sequence; 7.3 K-theory on algebraic varieties; 8.1 Stein manifold theory; 8.2 holomorphic vector bundles on polydisks; 9.1 concluding remarks; bibliography.
Originally published in 1974.
The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Kundenbewertungen
Tensor algebra, Analytic space, Complex vector bundle, Cohomology, Ring homomorphism, Automorphism, Presheaf (category theory), Ring (mathematics), Differentiable manifold, Homotopy, Cohomology ring, Variable (mathematics), Differential topology, Subset, De Rham cohomology, Resolution of singularities, Holomorphic sheaf, Irreducibility (mathematics), Topology, Theorem, Bott periodicity theorem, Isomorphism class, Chern class, Holomorphic function, Algebraic surface, Product topology, Special case, Sheaf of modules, Weierstrass preparation theorem, Algebraic geometry, Cohomology operation, Vector bundle, Homotopy group, Dimension (vector space), Holomorphic vector bundle, Tangent bundle, Algebraic variety, Sheaf (mathematics), Sheaf cohomology, Projective space, Algebraic curve, Codimension, Algebraic operation, Measure (mathematics), Module (mathematics), Hilbert's syzygy theorem, Epimorphism, Group homomorphism, Polynomial, Stein manifold, Riemann surface, Topological space, Zariski topology, Principal bundle, Mathematical induction, Lie derivative, Schwarz lemma, Differential form, Complex manifold, Divisor (algebraic geometry), Chow's theorem, Projective variety, Commutative diagram, Analytic continuation, Line bundle, Atiyah–Hirzebruch spectral sequence, Diagram (category theory), Exact sequence, Duality (mathematics), Cauchy's integral formula