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Aimed primarily at graduate students and
beginning researchers, this book provides an introduction to algebraic
geometry that is particularly suitable for those with no previous
contact with the subject and assumes only the standard background of
undergraduate algebra. It is developed from a masters course given at
the Université Paris-Sud, Orsay, and focusses on projective algebraic
geometry over an algebraically closed base field.
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.
Categories:Mathematics - Geometry and Topology
Content Type:Books
Year:2008
Edition:1
Language:english
Pages:263
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