Positivity in Algebraic Geometry I

Classical Setting: Line Bundles and Linear Series

Robert Lazarsfeld

388 pages, parution le 27/01/2005

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Résumé

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. Both volumes are also available as hardcover editions as Vols. 48 and 49 in the series "Ergebnisse der Mathematik und ihrer Grenzgebiete".

Written for: Graduate students and researchers in Algebraic Geometry and neighboring fields

Sommaire

Volume I

Part One: Ample Line Bundles and Linear Series
- Ample and Nef Line Bundles
- Linear Series
- Geometric Manifestations of Positivity
- Vanishing Theorems
- Local Positivity
- A. Projective Bundles
- B.Cohomology and Complexes

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Robert Lazarsfeld
Parution	27/01/2005
Nb. de pages	388
Format	15,5 x 23,5
Couverture	Broché
Poids	620g
Intérieur	Noir et Blanc
EAN13	9783540225287