This monograph provides a concise treatment of homology theory on algebraic varieties, beginning with linear sections, singular sections, and hyperplane sections of varieties. It explores Lefschetz's first and second theorems, proving the second theorem, and details the Poincar¨¦ formula and proof of invariant and relative cycles. The monograph is aimed at advanced undergraduate and graduate students and includes elaborate proofs across separate chapters with geometric descriptions and diagrams.
2. 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?€?? (more) 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 Poincar?? formula and
details of its proof, and invariant and relative cycles. (less)
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comment. Book Details ? Publisher: Dover Publications (October 27, 2014) Format: EPUB
Page count: 128 pages File size: 19.6 MB Protection: DRM Language: English Look for similar
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Abstract
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