Homology Theory on Algebraic Varieties

by Andrew H. Wallace

Overview

Concise and authoritative, this monograph is geared toward advanced undergraduate and graduate students. The main theorems whose proofs are given here were first formulated by Lefschetz and have since turned out to be of fundamental importance in the topological aspects of algebraic geometry. The proofs are fairly elaborate and involve a considerable amount of detail; therefore, some appear in separate chapters that include geometrical descriptions and diagrams.
The treatment begins with a brief introduction and considerations of linear sections of an algebraic variety as well as singular and hyperplane sections. Subsequent chapters explore Lefschetz's first and second theorems with proof of the second theorem, the Poincaré formula and details of its proof, and invariant and relative cycles.

Product Details

ISBN-13:	9780486799902
Publisher:	Dover Publications
Publication date:	09/27/2014
Series:	Dover Books on Mathematics
Sold by:	Barnes & Noble
Format:	eBook
Pages:	128
File size:	21 MB
Note:	This product may take a few minutes to download.

About the Author

Andrew H. Wallace (1926–2008) was Professor of Mathematics at the University of Pennsylvania, where he was Chairman of the Mathematics Department from 1968 to 1971. His other Dover books are Algebraic Topology: Homology and Cohomology; Differential Topology: First Steps; and An Introduction to Algebraic Topology.

Table of Contents

Concise and authoritative, this monograph is geared toward advanced undergraduate and graduate students. The main theorems whose proofs are given here were first formulated by Lefschetz and have since turned out to be of fundamental importance in the topological aspects of algebraic geometry. The proofs are fairly elaborate and involve a considerable amount of detail; therefore, some appear in separate chapters that include geometrical descriptions and diagrams.
The treatment begins with a brief introduction and considerations of linear sections of an algebraic variety as well as singular and hyperplane sections. Subsequent chapters explore Lefschetz's first and second theorems with proof of the second theorem, the Poincaré formula and details of its proof, and invariant and relative cycles.
Dover (2015) republication of the edition originally published by the Pergamon Press, London, 1958.
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