On rigidity of trinomial hypersurfaces and factorial trinomial varieties
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Trinomial varieties are affine varieties given by some special system of equations consisting of polynomials with three terms. Such varieties are total coordinate spaces of normal rational varieties with torus action of complexity one. For an affine variety X we consider the subgroup SAut(X) of the automorphism group generated by all algebraic subgroups isomorphic to the additive group of the ground field. An affine variety X is rigid if SAut(X) is trivial. In opposite an affine variety is flexible if SAut(X) acts transitively on the regular locus. Arzhantsev proved a criterium for a factorial trinomial hypersurface to be rigid. We give two generalizations of Arzhantsev's result: a criterium for an arbitrary trinomial hypersurface to be rigid and a criterium for a factorial trinomial variety to be rigid. Also a sufficient condition for a trinomial hypersurface to be flexible is obtained.
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Cited by 3 Pith papers
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$\mathbb T$-homogeneous locally nilpotent derivations of trinomial algebras
Trinomial algebras admit a description of their T-homogeneous locally nilpotent derivations under complexity-one torus actions.
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$\mathbb T$-homogeneous locally nilpotent derivations of trinomial algebras
The paper classifies T-homogeneous locally nilpotent derivations on trinomial algebras arising as Cox rings of complexity-one torus actions.
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Isotropy subgroups of homogeneous locally nilpotent derivations
Description of isotropy groups for maximal homogeneous locally nilpotent derivations on affine toric varieties and trinomial hypersurfaces, plus criteria to determine maximality.
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