Algebraic Geometry

An Introduction
1. Auflage. 2008
ISBN: 978-1-84800-055-1
Verlag: Springer

Buch, Englisch, 263 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 423 g

Reihe: Universitext

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; it assumes only the standard background of undergraduate algebra. It is developed from a masters course given at the Université Paris-Sud, Orsay, and focuses on projective algebraic geometry over an algebraically closed base field. The book starts with easily-formulated problems with non-trivial solutions 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, 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.

Zielgruppe

Research

Autoren/Hrsg.

Perrin, Daniel

Weitere Mitwirkende

Maclean, Catriona

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein
• Mathematik | Informatik Mathematik Algebra Elementare Algebra
• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie

Inhaltsverzeichnis

Affine 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.