Positivity in Algebraic Geometry I Classical Setting: Line Bundles and Linear Series |
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Author:
| Lazarsfeld, R. K. |
Series title: | Ergebnisse der Mathematik und Ihrer Grenzgebiete. 3. Folge / a Series of Modern Surveys in Mathematics Ser. |
ISBN: | 978-3-540-22533-1 |
Publication Date: | Aug 2004 |
Publisher: | Springer Berlin / Heidelberg
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Imprint: | Springer |
Book Format: | Hardback |
List Price: | USD $199.99 |
Book Description:
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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...
More Description
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.