Positivity in Algebraic Geometry - 1: Positivity in Algebraic Geometry I

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.

List of contents

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.

Summary

Two volume work containing a contemporary account on Positivity in Algebraic Geometry
A good deal of the material has not previously appeared in book form
Volume I is more elementary than Volume II and can be read without access to Volume II
Topics in Volume I: ample line bundles and linear series on a projective variety, the classical theorems of  Lefschetz and Bertini, vanishing theorems, local positivity
Contains many concrete examples, applications, and pointers to further developments

Product details

• Authors: R K Lazarsfeld, R. K Lazarsfeld, R. K. Lazarsfeld, R.K. Lazarsfeld, Robert Lazarsfeld
• Publisher: Springer, Berlin
• Languages: English
• Product format: Hardback
• Released: 29.09.2004
• EAN: 9783540225331
• ISBN: 978-3-540-22533-1
• No. of pages: 387
• Weight: 736 g
• Illustrations: XVIII, 387 p.
• Sets: Positivity in Algebraic Geometry; Positivity in Algebraic Geometry
• Series: Ergebnisse der Mathematik und ihrer Grenzgebiete; Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge; Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics; Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge; Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Arithmetic, algebra; Geometrie, C, geometry, Mathematics and Statistics, Algebraic Geometry, Multiplier Ideals, Vector Bundles, Vanishing Theorems