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

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by Phillip A. Griffiths & John Frank Adams
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Topics in Algebraic and Analytic Geometry. (MN-13): Notes From a Course of Phillip Griffiths by Phillip A. Griffiths & John Frank Adams

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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Ebook Details
Pages: 228
Size: 7.8 MB
Publisher: Princeton University Press
Date published:   2015
ISBN: 9781400869268 (DRM-PDF)

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This product is listed in the following categories:

Nonfiction > Mathematics > Geometry
Nonfiction > Mathematics > Geometry > Analytic

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Nonfiction > Mathematics > Calculus
Nonfiction > Mathematics > Geometry > Algebraic
Nonfiction > Mathematics > Group Theory
Nonfiction > Mathematics > Complex Analysis
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Nonfiction > Mathematics
Nonfiction > Mathematics > Geometry
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