Homology Theory on Algebraic Varieties

Nonfiction, Science & Nature, Mathematics, Algebra
Cover of the book Homology Theory on Algebraic Varieties by Andrew H. Wallace, Dover Publications
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Author: Andrew H. Wallace ISBN: 9780486799902
Publisher: Dover Publications Publication: October 27, 2014
Imprint: Dover Publications Language: English
Author: Andrew H. Wallace
ISBN: 9780486799902
Publisher: Dover Publications
Publication: October 27, 2014
Imprint: Dover Publications
Language: English

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.

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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.

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