BeschreibungThis introduction to algebraic geometry assumes only the standard background of undergraduate algebra and is particularly suitable for those with no previous contact with the subject. The book focusses on projective algebraic geometry over an algebraically closed base field. It 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.
InhaltsverzeichnisAffine algebraic sets.- Projective algebraic sets.- Sheaves and varieties.- Dimension.- Tangent spaces and singular points.- Bézout's theorem.- Sheaf cohomology.- Arithmetic genus of curves and the weak Riemann-Roch theorem.- Rational maps, geometric genus and rational curves.- Liaison of space curves.
PortraitProf. Dr. Daniel Perrin leitet das Institut für Angewandte Medienwissenschaft IAM der Zürcher Hochschule Winterthur. Seine Arbeitsschwerpunkte sind Medienlinguistik und Textproduktionsforschung.
PressestimmenFrom the reviews:"The book under review, Algebraic Geometry, by Daniel Perrin, is an introductory text on modern algebraic geometry. It is aimed to be the text for a first basic course for graduate students. ... is very nicely written (and very nicely translated into English too). ... Perrin has included many, many remarks aimed to explain and deconstruct definitions and theorems. I believe these remarks will be very valuable to the reader in order to gain the very much needed intuition for the theory." (Álvaro Lozano-Robledo, MathDL, May, 2008)"The book under review is the faithful translation into English of D. Perrin's popular French text 'Géométrie algébrique. Une introduction.' ... will be to the greatest benefit of the wide international community of students, teachers, and beginning researchers in the field of modern algebraic geometry. Also, we would like to emphasize again that this primer is perfectly suitable for a one-semester graduate course on the subject, and for profound self-study just as well." (Werner Kleinert, Zentralblatt MATH, Vol. 1132 (10), 2008)"This is the English translation of an outstanding textbook, originally published in French. ... Appendices contain a summary of results from commutative algebra used in this book and a short introduction to scheme theory. Anyone looking for a textbook on algebraic geometry that starts with the basics and presents a lot of material in a digestible way ... will find this volume an excellent choice." (Ch. Baxa, Monatshefte für Mathematik, Vol. 160 (4), July, 2010)
Untertitel: An Introduction. Originaltitel: Géometrie algébrique. 'uniext'. 8 schw. -w. Abbildungen, 8 schw. -w. Zeichnungen. Sprache: Englisch.
Verlag: Springer-Verlag GmbH
Erscheinungsdatum: Januar 2008
Übersetzer/Sprecher: Übersetzt von Catriona Maclean