Geometry of Higher Dimensional Algebraic Varieties

Released on by Thomas Peternell
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  • Geometry of Higher Dimensional Algebraic Varieties Book Detail

  • Author : Thomas Peternell
  • Release Date : 2012-12-06
  • Publisher : Birkhäuser
  • Genre : Mathematics
  • Pages : 221
  • ISBN 13 : 3034888937
  • File Size : 31,31 MB
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Geometry of Higher Dimensional Algebraic Varieties by Thomas Peternell PDF Summary

Book Description: 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.

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Higher-Dimensional Algebraic Geometry

Higher-Dimensional Algebraic Geometry

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The classification theory of algebraic varieties is the focus of this book. This very active area of research is still developing, but an amazing quantity of kn