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

Klappentext

This two-volume book 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. At least a third of the book is devoted to concrete examples, applications, and pointers to further developments. Most of the material in the present Volume II has not previously appeared in book form, and substantial parts are worked out here in detail for the first time. Both volumes are also available as hardcover editions as Vols. 48 and 49 in the series "Ergebnisse der Mathematik und ihrer Grenzgebiete."

Inhalt
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.