Topics in Algebraic and Analytic Geometry. (MN-13), Volume 13: Notes From a Course of Phillip Griffiths (Mathematical Notes, 13)

Griffiths, Phillip A.; Adams, John Frank

ISBN 10: 0691081514 / ISBN 13: 9780691081519

Published by Princeton University Press, 1974

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Bibliographic Details

• Title: Topics in Algebraic and Analytic Geometry. (MN-13), Volume 13: Notes From a Course of Phillip Griffiths (Mathematical Notes, 13)
• Publisher: Princeton University Press
• Publication Date: 1974
• Language: English
• ISBN 10: 0691081514
• ISBN 13: 9780691081519
• Binding: Paperback
• Condition: New
• Weight: 12 ounces

About this title

Synopsis

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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