Homology Theory on Algebraic Varieties (Dover Books on Mathematics)

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About Homology Theory On Algebraic Varieties

Product Description 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. From the Back Cover 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.See every Dover book in print atwww.doverpublications.com 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.