Geometry of Higher Dimensional Algebraic Varieties

Thomas Peternell, Joichi Miyaoka (Autoren)

Buch | Softcover

VI, 218 Seiten

1997 | 1997
Springer Basel (Verlag)
978-3-7643-5490-9 (ISBN)

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This book is based on lecture notes of a seminar of the Deutsche Mathematiker Vereinigung held by the authors at Oberwolfach from April 2 to 8, 1995. It gives an introduction to the classification theory and geometry of higher dimensional complex-algebraic varieties, focusing on the tremendeous developments of the sub ject in the last 20 years. The work is in two parts, with each one preceeded by an introduction describing its contents in detail. Here, it will suffice to simply ex plain how the subject matter has been divided. Cum grano salis one might say that Part 1 (Miyaoka) is more concerned with the algebraic methods and Part 2 (Peternell) with the more analytic aspects though they have unavoidable overlaps because there is no clearcut distinction between the two methods. Specifically, Part 1 treats the deformation theory, existence and geometry of rational curves via characteristic p, while Part 2 is principally concerned with vanishing theorems and their geometric applications. Part I Geometry of Rational Curves on Varieties Yoichi Miyaoka RIMS Kyoto University 606-01 Kyoto Japan Introduction: Why Rational Curves? This note is based on a series of lectures given at the Mathematisches Forschungsin stitut at Oberwolfach, Germany, as a part of the DMV seminar "Mori Theory". The construction of minimal models was discussed by T.

I Geometry of Rational Curves on Varieties.- Introduction: Why Rational Curves.- Lecture I: Deformations and Rational Curves.- Lecture II: Construction of Non-Trivial Deformations via Frobenius.- Lecture III: Foliations and Purely Inseparable Coverings.- Lecture IV: Abundance for Minimal 3-Folds.- Lecture V: Rationally Connected Fibrations and Applications.- References.- II An Introduction to the Classification of Higherdimensional Complex Varieties.- Preface.- Prerequisites.- References.

"Contains nice historical notes and exercises... Many examples are given to illustrate the theory... Beautifully written [with] up-to-date references to the subjects... Highly recommended."

--ZAA

Erscheint lt. Verlag	20.3.1997
Reihe/Serie	Oberwolfach Seminars
Zusatzinfo	VI, 218 p. 2 illus.
Verlagsort	Basel
Sprache	englisch
Maße	178 x 254 mm
Gewicht	432 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	Algebra • Algebraic Geometry • Algebraic Varieties • Algebraische Geometrie • algebraische Varietät • Calculus • complex analyisis • Complex Analysis • Geometry • Hardcover, Softcover / Mathematik/Allgemeines, Lexika • HC/Mathematik/Geometrie • Kurven • manifold • Mannigfaltigkeit (Mathematik) • Mathematik • Proof • Theorem
ISBN-10	3-7643-5490-9 / 3764354909
ISBN-13	978-3-7643-5490-9 / 9783764354909
Zustand	Neuware