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

Author: R Lazarsfeld
Publisher: Berlin, Germany : Springer, 2004.
Series: Ergebnisse der Mathematik und ihrer Grenzgebiete, v. 48.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: R Lazarsfeld
ISBN: 9783642188084 3642188087
OCLC Number: 1002125909
Description: 1 online resource (xviii, 387 pages)
Contents: 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.
Series Title: Ergebnisse der Mathematik und ihrer Grenzgebiete, v. 48.
Responsibility: Robert Lazarsfeld.

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.

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