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Flops

Published online by Cambridge University Press:  22 January 2016

János Kollár
János Kollár*
Affiliation:
Institute for Advanced Study, Princeton, New Jersey, U.S.A.
*
University of Utah, Salt Lake City UT 84112, U.S.A.
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The aim of this note is to study birational transformations of three-folds with nef canonical classes. One would like to write any such map as a composite of certain simple and basic transformations.

A special case was first considered by Kulikov [Ku] and later extensively studied by several authors. The next main conceptual step was Reid’s study [R2] of small resolutions of terminal threefold singularities. He obtained the elementary birational transformations as follows: find a copy of such a small resolution inside the threefold and then replace it with another resolution. This approach was extended by Kawamata [K3] to canonical singularities.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 113 , March 1989 , pp. 15 - 36
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1989

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