R. K. Lazarsfeld

Positivity in Algebraic Geometry I (eBook, PDF)

Classical Setting: Line Bundles and Linear Series

• Format: PDF

Produktbeschreibung

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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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 387
• Erscheinungstermin: 25. Juli 2017
• Englisch
• ISBN-13: 9783642188084
• Artikelnr.: 54789462

Autorenporträt

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

Inhaltsangabe

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.