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.

The **Princeton Legacy Library** makes use of the newest print-on-demand know-how to back make to be had formerly out-of-print books from the celebrated backlist of Princeton college Press. those paperback variations guard the unique texts of those vital books whereas providing them in sturdy paperback variants. The target of the Princeton Legacy Library is to tremendously bring up entry to the wealthy scholarly historical past present in the millions of books released by means of Princeton college Press due to the fact its founding in 1905.