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.
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