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Plane Algebraic Curves Volume 15 by Gerd Fischer is a mathematics available to read on EtoBox.

What is Plane Algebraic Curves Volume 15 about?

The study of the zeroes of polynomials, which for one variable is essentially algebraic, becomes a geometric theory for several variables. In this book, Fischer looks at the classic entry point to the subject: plane algebraic curves. Here one quickly sees the mix of algebra and geometry, as well as analysis and topology, that is typical of complex algebraic geometry, but without the need for advanced techniques from commutative algebra or the abstract machinery of sheaves and schemes. In the first half of this book, Fischer introduces some elementary geometrical aspects, such as tangents, singularities, inflection points, and so on. The main technical tool is the concept of intersection multiplicity and Bézout's theorem. This part culminates in the beautiful PlÃ1⁄4cker formulas, which relate the various invariants introduced earlier. The second part of the book is essentially a detailed outline of modern methods of local analytic geometry in the context of complex curves. This provides the stronger tools needed for a good understanding of duality and an efficient means of computing intersection multiplicities introduced earlier. Thus, we meet rings of power series, germs of c

Who reads Plane Algebraic Curves Volume 15?

Author

Gerd Fischer

Publisher

American Mathematical Society

Published

2001

Language

EN

ISBN

9780821821220

Category

mathematics

Subjects

Mathematics, Stem

Rating

5 / 5 (2 ratings)

Updated

2026-03-14