Positivity in Algebraic Geometry - Volume 1, Classical Setting: Line Bundles and Linear Series (Broché)

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 1 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 at least a third of the book is devoted to concrete examples, applications, and pointers to further developments. Volume 1 is more elementary than Volume II, and, for the most part, it can be read without access to Volume 11. Both volumes are also available as hardcover editions as Vols. 48 and 49 in the series "Ergebnisse der Mathematik and ihrer Grenzgebiete".