Classification of Higher Dimensional Algebraic Varieties

Classification of Higher Dimensional Algebraic Varieties by Christopher D. Hacon, Sándor Kovács.

This book focuses on recent advances in the classification of complex projective varieties. It is divided into two parts. The first part gives a detailed account of recent results in the minimal model program. In particular, it contains a complete proof of the theorems on the existence of flips, on...

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Bibliographic Details
Main Authors: Hacon, Christopher D. (Author), Kovács, Sándor (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Basel : Birkhäuser Basel : Imprint: Birkhäuser, 2010.
Edition:1st ed. 2010.
Series:Oberwolfach Seminars, 41
Springer eBook Collection.
Subjects:
Algebraic geometry.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • Basics
  • Preliminaries
  • Singularities
  • Recent advances in the minimal model program
  • The main result
  • Multiplier ideal sheaves
  • Finite generation of the restricted algebra
  • Log terminal models
  • Non-vanishing
  • Finiteness of log terminal models
  • Compact moduli spaces of canonically polarized varieties
  • Moduli problems
  • Hilbert schemes
  • The construction of the moduli space
  • Families and moduli functors
  • Singularities of stable varieties
  • Subvarieties of moduli spaces.

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