Algebraic Geometry : An Introduction
Publication year: 2008
ISBN: 978-1-84800-056-8
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The book starts with easily-formulated problems with non-trivial solutions – for example, Bézout’s theorem and the problem of rational curves – and uses these problems to introduce the fundamental tools of modern algebraic geometry: dimension; singularities; sheaves; varieties; and cohomology. The treatment uses as little commutative algebra as possible by quoting without proof (or proving only in special cases) theorems whose proof is not necessary in practice, the priority being to develop an understanding of the phenomena rather than a mastery of the technique. A range of exercises is provided for each topic discussed, and a selection of problems and exam papers are collected in an appendix to provide material for further study.
Subject: Mathematics and Statistics, Algebra, Arithmetic, Riemann-Roch theorem, algebraic geometry, cohomology, curves, dimension, geometry, projective geometry, proof, sheaves, singular points, theorem
