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＜E-Book＞
Geometry of Higher Dimensional Algebraic Varieties / by Thomas Peternell, Joichi Miyaoka
(Oberwolfach Seminars. ISSN:22965041 ; 26)

Edition	1st ed. 1997.
Publisher	(Basel : Birkhäuser Basel : Imprint: Birkhäuser)
Year	1997
Size	VI, 218 p. 2 illus : online resource
Authors	*Peternell, Thomas author Miyaoka, Joichi author SpringerLink (Online service)
Subjects	LCSH:Algebraic geometry LCSH:Geometry FREE:Algebraic Geometry FREE:Geometry
Notes	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 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 HTTP:URL=https://doi.org/10.1007/978-3-0348-8893-6

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