Complete toric varieties with reductive automorphism group
arXiv:math/0407491 · doi:10.1007/s00209-005-0880-z
Abstract
We give equivalent and sufficient criteria for the automorphism group of a complete toric variety, respectively a Gorenstein toric Fano variety, to be reductive. In particular we show that the automorphism group of a Gorenstein toric Fano variety is reductive, if the barycenter of the associated reflexive polytope is zero. Furthermore a sharp bound on the dimension of the reductive automorphism group of a complete toric variety is proven by studying the set of Demazure roots.
AMS-LaTeX, 20 pages with 1 figure
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Cited by in corpus (18)
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- Integral Cohomology and Mirror Symmetry for Calabi-Yau 3-folds
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- Examples of non-symmetric Kähler-Einstein toric Fano manifolds
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- On toric geometry and K-stability of Fano varieties
- Twisted forms of toric varieties
- Favourable modules: Filtrations, polytopes, Newton-Okounkov bodies and flat degenerations
- Root subgroups on affine spherical varieties
- Additive group actions on affine T-varieties of complexity one in arbitrary characteristic
- Lattice width directions and Minkowski's 3^d-theorem
- Toric Fano manifolds with nef tangent bundles
- Gale duality and homogeneous toric varieties
- Isotriviality and the space of morphisms on projective varieties
- Foldable fans, cscK surfaces and local K-moduli
- Examples on Loewy filtrations and K-stability of Fano varieties with non-reductive automorphism groups
- Lattices generated by skeletons of reflexive polytopes