Positivity in Algebraic Geometry I : Classical Setting: Line Bundles and Linear Series

R. K. Lazarsfeld

ISBN 10: 3540225331 / ISBN 13: 9783540225331

Published by Springer, Springer Spektrum, 2004

About this Item

Druck auf Anfrage Neuware - Printed after ordering - 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.

Seller Inventory # 9783540225331

Bibliographic Details

• Title: Positivity in Algebraic Geometry I : Classical Setting: Line Bundles and Linear Series
• Publisher: Springer, Springer Spektrum
• Publication Date: 2004
• Language: English
• ISBN 10: 3540225331
• ISBN 13: 9783540225331
• Binding: Buch
• Condition: Neu
• Dimensions: 241W x 160H x 27D millimeters 241 millimeters width by 160 millimeters height by 27 millimeters depth
• Weight: 776 grams

About this title

Synopsis

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.

Review

From the reviews:

"This ??? book offers a comprehensive, up-to-date account on ampleness and positivity in complex algebraic geometry. ??? The book contains a wealth of material and aims at readers with a certain overview in complex algebraic geometry. ??? the text never gets bogged down in technicalities, and is a pleasure to read. The presentation nicely reveals historical developments and mathematical interplay between various results. ??? A fine book indeed." (Stefan Schr??er, Zentralblatt MATH, Vol. 1066, 2005)

From the reviews:

"This a ] book offers a comprehensive, up-to-date account on ampleness and positivity in complex algebraic geometry. a ] The book contains a wealth of material and aims at readers with a certain overview in complex algebraic geometry. a ] the text never gets bogged down in technicalities, and is a pleasure to read. The presentation nicely reveals historical developments and mathematical interplay between various results. a ] A fine book indeed." (Stefan SchrAer, Zentralblatt MATH, Vol. 1066, 2005)