Positivity in Algebraic Geometry: Vol.1 Positivity in Algebraic Geometry I
Classical Setting: Line Bundles and Linear Series
(Sprache: Englisch)
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...
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Klappentext zu „Positivity in Algebraic Geometry: Vol.1 Positivity in Algebraic Geometry I “
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.
Inhaltsverzeichnis zu „Positivity in Algebraic Geometry: Vol.1 Positivity in Algebraic Geometry I “
Part One: Ample Line Bundles and Linear Series.- Introduction to Part One.- Ample Nef Line Bundles.- Linear Series.- Geometric Manifestations of Positivity.- Vanishing Theorems.- Local Positivity.- Appendices.- References.- Glossary of Notation.- Index.
Bibliographische Angaben
- Autor: R.K. Lazarsfeld
- 2007, Softcover reprint of the original 1st ed. 2004, 387 Seiten, 25 Abbildungen, Maße: 15,5 x 23,5 cm, Kartoniert (TB), Englisch
- Verlag: Springer
- ISBN-10: 3540225285
- ISBN-13: 9783540225287
- Erscheinungsdatum: 10.04.2007
Sprache:
Englisch
Rezension zu „Positivity in Algebraic Geometry: Vol.1 Positivity in Algebraic Geometry I “
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)
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