Griffiths / Adams Topics in Algebraic and Analytic Geometry

Notes From a Course of Phillip Griffiths
1. Auflage 2015
ISBN: 978-1-4008-6926-8
Verlag: De Gruyter
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, Band 13, 228 Seiten

Reihe: Mathematical NotesPrinceton Legacy Library

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.

The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Autoren/Hrsg.

Griffiths, Phillip A.

Adams, John Frank

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Analytische Geometrie

Inhaltsverzeichnis

Frontmatter, pg. i
Introduction, pg. iii
Contents, pg. v
Chapter One, pg. 1
Chapter Two, pg. 23
Chapter Three, pg. 56
Chapter Four, pg. 73
Chapter Five, pg. 83
Chapter Six, pg. 136
Chapter Seven, pg. 154
Chapter Eight, pg. 196
Chapter Nine, pg. 215
Bibliography, pg. 217