Positivity in Algebraic Geometry II: Positivity for Vector Bundles, and Multiplier Ideals

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R.K. Lazarsfeld

Positivity in Algebraic Geometry II

Positivity for Vector Bundles, and Multiplier Ideals

R.K. Lazarsfeld

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English

Springer Verlag
01 April 2004

Mathematics & Sciences; Algebraic geometry

Series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics

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 edition as Vols. 48 and 49 in the series ""Ergebnisse der Mathematik und ihrer Grenzgebiete"".

By: R.K. Lazarsfeld
Imprint: Springer Verlag
Country of Publication: Germany
Dimensions: Height: 235mm, Width: 155mm, Spine: 21mm
Weight: 1.250kg
ISBN: 9783540225317
ISBN 10: 3540225315
Series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
Pages: 404
Publication Date: 01 April 2004
Audience: College/higher education , Professional and scholarly , Further / Higher Education , Undergraduate
Format: Paperback
Publisher's Status: Active

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.

Reviews for Positivity in Algebraic Geometry II: Positivity for Vector Bundles, and Multiplier Ideals

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