Positivity in Algebraic Geometry - 2: Positivity in Algebraic Geometry II

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.
Whereas Volume I is more elementary, the present Volume II is more at the research level and somewhat more specialized. Both volumes are also available as hardcover editionas Vols. 48 and 49 in the series "Ergebnisse der Mathematik und ihrer Grenzgebiete".

List of contents

Notation and Conventions.- Two: Positivity for Vector Bundles.- 6 Ample and Nef Vector Bundles.- 7 Geometric Properties of Ample Bundles.- 8 Numerical Properties of Ample Bundles.- Three: Multiplier Ideals and Their Applications.- 9 Multiplier Ideal Sheaves.- 10 Some Applications of Multiplier Ideals.- 11 Asymptotic Constructions.- References.- Glossary of Notation.

Summary

Two volume work containing a contemporary account on "Positivity in Algebraic Geometry"
Both volumes also available as hardcover editions as Vols. 48 and 49 in the series "Ergebnisse der Mathematik und ihrer Grenzgebiete"
A good deal of the material has not previously appeared in book form
Volume II is more at the research level and somewhat more specialized than Volume I
Volume II contains a survey of positivity for vector bundles, and moves on to a systematic development of the theory of multiplier ideals and their applications
Contains many concrete examples, applications, and pointers to further developments

Report

From the reviews:

"The main theme of this ... monograph is a comprehensive description of the fields of complex algebraic geometry connected with the notion of positivity. ... The book is written for mathematicians interested in the modern development of algebraic geometry." (EMS Newsletter, September, 2006)

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: 9783540225348
• ISBN: 978-3-540-22534-8
• No. of pages: 385
• Dimensions: 157 mm x 242 mm x 28 mm
• Weight: 799 g
• Illustrations: XVII, 385 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