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MARC 21

Algebraic Geometry: An Introduction
Tag	Description
020	$a9781848000568
082	$a516.35
099	$aOnline Resource: Springer
100	$aPerrin, Daniel.
245	$aAlgebraic Geometry$h[Ebook]$bAn Introduction$cby Daniel Perrin ; translated from the French by Catriona Maclean
260	$aLondon$bSpringer$c2008.
300	$ax, 258 pages$bonline resource.
336	$atext
338	$aonline resource
440	$aUniversitext
505	$aForeword -- Notation -- Introduction -- Affine algebraic sets -- Projective algebraic sets -- Sheaves and varieties -- Dimension -- Tangent spaces and singular points -- Bézout's theorem -- Sheaf cohomology -- Arithmetic genus of curves -- Rational maps and geometric genus -- Liaison of space curves -- Appendices: Summary of useful results from algebra -- Schemes -- Problems -- References -- Index -- Index of notation.
520	$aAimed 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 â 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.
538	$aOnline access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
710	$aSpringerLink (Online service)
830	$aUniversitext
856	$uhttp://dx.doi.org/10.1007/978-1-84800-056-8