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On the classification of 3-dimensional SL2(ℂ)-varieties

Published online by Cambridge University Press:  22 January 2016

Stefan Kebekus
Stefan Kebekus*
Affiliation:
Mathematisches Institut der Universität Bayreuth, 95440 Bayreuth, Germany, FAX: +49 (0)921/55-2785 stefan.kebekus@uni-bayreuth.de
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Abstract

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In the present work we describe 3-dimensional complex SL2-varieties where the generic SL2-orbit is a surface. We apply this result to classify the minimal 3-dimensional projective varieties with Picard-number 1 where a semisimple group acts such that the generic orbits are 2-dimensional.

This is an ingredient of the classification [Keb99] of the 3-dimensional relatively minimal quasihomogeneous varieties where the automorphism group is not solvable.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 157 , 2000 , pp. 129 - 147
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2000

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