R. K. Lazarsfeld

Positivity in Algebraic Geometry II (eBook, PDF)

Positivity for Vector Bundles, and Multiplier Ideals

• Format: PDF

Produktbeschreibung

This two-volume book 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. At least a third of the book is devoted to concrete examples, applications, and pointers to further developments. Most of the material in the present Volume II has not previously appeared in book form, and substantial parts are worked out here in detail for the first time. Both volumes are also available as hardcover editions as Vols. 48 and 49 in the series "Ergebnisse der Mathematik und ihrer Grenzgebiete."

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 385
• Erscheinungstermin: 25. Juli 2017
• Englisch
• ISBN-13: 9783642188107
• Artikelnr.: 54793020

Autorenporträt

R.K. Lazarsfeld, University of Michigan, Ann Arbor, MI, USA

Inhaltsangabe

Notation and Conventions.- Two: Positivity for Vector Bundles.- 6 Ample and Nef Vector Bundles.- 7 Geometric Properties of Ample Bundles.- 8 Numerical Properties of Ample Bundles.- Three: Multiplier Ideals and Their Applications.- 9 Multiplier Ideal Sheaves.- 10 Some Applications of Multiplier Ideals.- 11 Asymptotic Constructions.- References.- Glossary of Notation.

Rezensionen

From the reviews:

"The main theme of this ... monograph is a comprehensive description of the fields of complex algebraic geometry connected with the notion of positivity. ... The book is written for mathematicians interested in the modern development of algebraic geometry."

(EMS Newsletter, September, 2006)