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ON TORUS ACTIONS OF HIGHER COMPLEXITY

Published online by Cambridge University Press:  31 October 2019

JÜRGEN HAUSEN
Affiliation:
Fachbereich Mathematik, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany; juergen.hausen@uni-tuebingen.de, hische@math.uni-tuebingen.de
CHRISTOFF HISCHE
Affiliation:
Fachbereich Mathematik, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany; juergen.hausen@uni-tuebingen.de, hische@math.uni-tuebingen.de
MILENA WROBEL
Affiliation:
Institut für Mathematik, Universität Oldenburg, 26111 Oldenburg, Germany; milena.wrobel@uni-oldenburg.de

Abstract

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We systematically produce algebraic varieties with torus action by constructing them as suitably embedded subvarieties of toric varieties. The resulting varieties admit an explicit treatment in terms of toric geometry and graded ring theory. Our approach extends existing constructions of rational varieties with torus action of complexity one and delivers all Mori dream spaces with torus action. We exhibit the example class of ‘general arrangement varieties’ and obtain classification results in the case of complexity two and Picard number at most two, extending former work in complexity one.

Type
Research Article
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s) 2019

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