SMF

Flips and abundance for algebraic threefolds

Flips and abundance for algebraic threefolds

János KOLLÁR
Flips and abundance for algebraic threefolds
  • Année : 1992
  • Tome : 211
  • Format : Papier, Électronique
  • Langue de l'ouvrage :
    Anglais
  • Class. Math. : 14-02, 14E30, 14E35, 14J40, 14J60, 14C40
  • Nb. de pages : 272
  • ISSN : 0303-1179
  • DOI : 10.24033/ast.198

This work consists of twenty-three lectures which comprised a summer seminar in three dimensional algebraic geometry. The seminar took place during the month of August, 1991 at the University of Utah. It was a continuation of the first summer seminar whose notes appeared in Astérisque, volume 166. The aim of the seminar was to explore and simplify recent developments in the theory of algebraic threefolds. The study of algebraic surfaces starts with two fundamental theorems : every nonruled surface is birational to a minimal surface, and on a minimal surface a suitable multiple of the canonical divisor determines a base point free linear system. Recently both of these results have been generalized to dimension three. We present a detailed and fairly selfcontained exposition of these developments. One of our main aims is to present the proofs in a way which points to the possibility of generalizing these results to higher dimensions.

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