Positivity in Algebraic Geometry I

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.

Volume I is more elementary than Volume II, and, for the most part, it can be read without access to Volume II.

Notation and Conventions. - One: Ample Line Bundles and Linear Series. - to Part One. - 1 Ample and Nef Line Bundles. - 2 Linear Series. - 3 Geometric Manifestations of Positivity. - 4 Vanishing Theorems. - 5 Local Positivity. - Appendices. - A Projective Bundles. - B Cohomology and Complexes. - B. 1 Cohomology. - B. 2 Complexes. - References. - Glossary of Notation.