Geometry of Higher Dimensional Algebraic Varieties

Yoichi Miyaoka

ISBN 10: 3764354909 / ISBN 13: 9783764354909

Published by Springer, Basel, Birkhäuser Basel Mrz 1997, 1997

About this Item

This item is printed on demand - it takes 3-4 days longer - Neuware -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. 218 pp. Englisch.

Seller Inventory # 9783764354909

Bibliographic Details

• Title: Geometry of Higher Dimensional Algebraic Varieties
• Publisher: Springer, Basel, Birkhäuser Basel Mrz 1997
• Publication Date: 1997
• Language: English
• ISBN 10: 3764354909
• ISBN 13: 9783764354909
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 25.4W x 17.8H x 0D centimeters 25.4 centimeters width by 17.8 centimeters height by 0 centimeters depth
• Weight: 446 grams

About this title

Synopsis

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.

Review

"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