Homology Theory on Algebraic Varieties (Dover Books on Mathematics)

Book Details

• Publisher: Dover

• Author: Wallace, Andrew H.

• Language: English

• Edition: Illustrated

• ISBN: 9780486787848

• Pages: 128

• Cover: Paperback

About the Book

Lefschetz Theorems: A Topological Approach by Andrew H. Wallace is a concise and authoritative monograph tailored for advanced undergraduate and graduate students of algebraic geometry. The book focuses on Lefschetz's celebrated theorems, which have become foundational in understanding the topological aspects of algebraic geometry. Wallace provides in-depth proofs of these key theorems, elucidating their significance and offering a comprehensive treatment of the subject.

The text starts with a brief introduction to algebraic varieties and linear sections, progressing through the intricacies of Lefschetz’s first and second theorems. The author includes the geometrical descriptions, diagrams, and detailed proofs essential to grasp the core concepts. Special attention is paid to the Poincaré formula and the related invariant and relative cycles, offering a clear and complete exploration of these essential components.

Whether you are delving into the study of algebraic geometry for the first time or refining your understanding of Lefschetz's theorems, this work serves as both an introduction and an advanced resource. The clarity of its explanations and the inclusion of geometric illustrations make it an indispensable guide for anyone exploring the intersection of topology and algebraic geometry.