Positivity in Algebraic Geometry I
Springer Berlin (Verlag)
978-3-540-22533-1 (ISBN)
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.
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.
| Erscheint lt. Verlag | 24.8.2004 |
|---|---|
| Reihe/Serie | Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics |
| Zusatzinfo | XVIII, 387 p. |
| Verlagsort | Berlin |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 735 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| Schlagworte | Algebraic Varieties • Algebraische Geometrie • Linear Series • line bundles • Multiplier Ideals • Vanishing Theorems • Vector Bundles |
| ISBN-10 | 3-540-22533-1 / 3540225331 |
| ISBN-13 | 978-3-540-22533-1 / 9783540225331 |
| Zustand | Neuware |
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