Lazarsfeld Positivity in Algebraic Geometry I

Classical Setting: Line Bundles and Linear Series
1. Auflage 2004
ISBN: 978-3-642-18808-4
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 48, 387 Seiten, eBook

Reihe: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge

This two volume work on Positivity in Algebraic Geometry contains a contemporary account of a body of work in complex algebraic geometry loosely centered around the theme of positivity. Topics in Volume I include ample line bundles and linear series on a projective variety, the classical theorems of Lefschetz and Bertini and their modern outgrowths, vanishing theorems, and local positivity. Volume II begins with a survey of positivity for vector bundles, and moves on to a systematic development of the theory of multiplier ideals and their applications. A good deal of this material has not previously appeared in book form, and substantial parts are worked out here in detail for the first time. At least a third of the book is devoted to concrete examples, applications, and pointers to further developments. Volume I is more elementary than Volume II, and, for the most part, it can be read without access to Volume II.

Zielgruppe

Research

Autoren/Hrsg.

Lazarsfeld, R.K.

Inhaltsverzeichnis

Notation and Conventions.- One: Ample Line Bundles and Linear Series.- to Part One.- 1 Ample and Nef Line Bundles.- 2 Linear Series.- 3 Geometric Manifestations of Positivity.- 4 Vanishing Theorems.- 5 Local Positivity.- Appendices.- A Projective Bundles.- B Cohomology and Complexes.- B.1 Cohomology.- B.2 Complexes.- References.- Glossary of Notation.