Positivity in Algebraic Geometry II: Positivity for Vector Bundles, and Multiplier Ideals (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 49);

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