By Phillip A. Griffiths, John Frank Adams
This quantity bargains a scientific remedy of convinced uncomplicated elements of algebraic geometry, offered from the analytic and algebraic issues of view. The notes specialise in comparability theorems among the algebraic, analytic, and non-stop categories.
Contents comprise: 1.1 sheaf conception, ringed areas; 1.2 neighborhood constitution of analytic and algebraic units; 1.3 P
n 2.1 sheaves of modules; 2.2 vector bundles; 2.3 sheaf cohomology and computations on P
n; 3.1 greatest precept and Schwarz lemma on analytic areas; 3.2 Siegel's theorem; 3.3 Chow's theorem; 4.1 GAGA; 5.1 line bundles, divisors, and maps to P
n; 5.2 Grassmanians and vector bundles; 5.3 Chern sessions and curvature; 5.4 analytic cocycles; 6.1 K-theory and Bott periodicity; 6.2 K-theory as a generalized cohomology concept; 7.1 the Chern personality and obstruction concept; 7.2 the Atiyah-Hirzebruch spectral series; 7.3 K-theory on algebraic forms; 8.1 Stein manifold idea; 8.2 holomorphic vector bundles on polydisks; 9.1 concluding feedback; bibliography.
Originally released in 1974.
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