"The book under review is a reprint of Mumford's famous Harvard lecture notes, widely used by the few past generations of algebraic geometers. Springer-Verlag has done the mathematical community a service by making these notes available once again.... The informal style and frequency of examples make the book an excellent text." (Mathematical Reviews)
Reihe
Auflage
1st ed. 1988. 2nd printing
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Research
Illustrationen
Maße
Höhe: 24.4 cm
Breite: 17 cm
Gewicht
ISBN-13
978-3-540-50497-9 (9783540504979)
DOI
10.1007/978-3-662-21581-4
Schweitzer Klassifikation
Varieties.- Some algebra.- Irreducible algebraic sets.- Definition of a morphism: I.- Sheaves and affine varieties.- Definition of prevarieties and morphism.- Products and the Hausdorff Axiom.- Dimension.- The fibres of a morphism.- Complete varieties.- Complex varieties.- Preschemes.- Spec (R).- The category of preschemes.- Varieties are preschemes.- Fields of definition.- Closed subpreschemes.- The functor of points of a prescheme.- Proper morphisms and finite morphisms.- Specialization.- Local Properties of Schemes.- Quasi-coherent modules.- Coherent modules.- Tangent cones.- Non-singularity and differentials.- Étale morphisms.- Uniformizing parameters.- Non-singularity and the UFD property.- Normal varieties and normalization.- Zariski's Main Theorem.- Flat and smooth morphisms.
