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ON TORUS ACTIONS OF HIGHER COMPLEXITY

Part of: Surfaces and higher-dimensional varieties Special varieties Algebraic groups

Published online by Cambridge University Press:  31 October 2019

JÜRGEN HAUSEN ,
CHRISTOFF HISCHE  and
MILENA WROBEL
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.

MSC classification

Primary: 14L30: Group actions on varieties or schemes (quotients) 14M25: Toric varieties, Newton polyhedra 14J45: Fano varieties
Type
Research Article
Information
Forum of Mathematics, Sigma , Volume 7 , 2019 , e38
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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