Positivity in algebraic geometry I : classical setting: line bundles and linear series

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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. �Read more... Abstract: 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 Front Matter ....Pages I-XVIII Notation and Conventions (Robert Lazarsfeld)....Pages 1-2 Front Matter ....Pages 3-3 Introduction to Part One (Robert Lazarsfeld)....Pages 5-6 Ample and Nef Line Bundles (Robert Lazarsfeld)....Pages 7-119 Linear Series (Robert Lazarsfeld)....Pages 121-183 Geometric Manifestations of Positivity (Robert Lazarsfeld)....Pages 185-237 Vanishing Theorems (Robert Lazarsfeld)....Pages 239-267 Local Positivity (Robert Lazarsfeld)....Pages 269-312 Back Matter ....Pages 313-387