The automorphism group of a variety with torus action of complexity one

Ivan Arzhantsev; Juergen Hausen; Elaine Herppich; Alvaro Liendo

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arXiv · 1202.4568

The automorphism group of a variety with torus action of complexity one

Ivan Arzhantsev·Juergen Hausen·Elaine Herppich·Alvaro Liendo

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Abstract

We consider a normal complete rational variety with a torus action of complexity one. In the main results, we determine the roots of the automorphism group and give an explicit description of the root system of its semisimple part. The results are applied to the study of almost homogeneous varieties. For example, we describe all almost homogeneous (possibly singular) del Pezzo k*-surfaces of Picard number one and all almost homogeneous (possibly singular) Fano threefolds of Picard number one having a reductive automorphism group with two-dimensional maximal torus.

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Ivan Arzhantsev, Juergen Hausen, Elaine Herppich, Alvaro Liendo. 2012-02-21. The automorphism group of a variety with torus action of complexity one. https://arxiv.org/abs/1202.4568

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