3264 and All That A Second Course in Algebraic Geometry
3264 and All That: A Second Course in Algebraic Geometry by David Eisenbud, published by Cambridge University Press on April 14, 2016, is a comprehensive text designed for students pursuing a deeper understanding of algebraic geometry. This edition spans 616 pages and is presented in English, focusing on concrete questions from enumerative geometry and intersection theory. The book aims to equip readers with the intuition and techniques necessary to tackle geometric problems, explaining key concepts such as rational equivalence, Chow rings, Schubert calculus, and Chern classes.
Readers will find a wealth of examples throughout the text, many of which are accompanied by exercises with solutions available online. The book emphasizes the enumeration of solutions to systems of polynomial equations in multiple variables, tracing the historical significance of intersection theory from Leibniz to Poincaré. By exploring these foundational topics in mathematics, including algebra, geometry, and topology, this work serves as a valuable resource for those looking to advance their knowledge in these interconnected fields.
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This book can form the basis of a second course in algebraic geometry. As motivation, it takes concrete questions from enumerative geometry and intersection theory, and provides intuition and technique, so that the student develops the ability to solve geometric problems. The authors explain key ideas, including rational equivalence, Chow rings, Schubert calculus and Chern classes, and readers will appreciate the abundant examples, many provided as exercises with solutions available online. Intersection is concerned with the enumeration of solutions of systems of polynomial equations in several variables. It has been an active area of mathematics since the work of Leibniz. Chasles’ nineteenth-century calculation that there are 3264 smooth conic plane curves tangent to five given general conics was an important landmark, and was the inspiration behind the title of this book. Such computations were motivation for Poincaré’s development of topology, and for many subsequent theories, so that intersection theory is now a central topic of modern mathematics.
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