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ON TORUS ACTIONS OF HIGHER COMPLEXITY

  • JÜRGEN HAUSEN (a1), CHRISTOFF HISCHE (a1) and MILENA WROBEL (a2)

Abstract

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.

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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.

References

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ON TORUS ACTIONS OF HIGHER COMPLEXITY

  • JÜRGEN HAUSEN (a1), CHRISTOFF HISCHE (a1) and MILENA WROBEL (a2)

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