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Working paper

The automorphism group of a rigid affine variety

arxiv.org. math. Cornell University, 2016. No.  arXiv:1607.03472.
An algebraic variety X is rigid if it admits no nontrivial action of the additive group of the ground field. We prove that the automorphism group Aut(X) of a rigid affine variety contains a unique maximal torus T. If the grading on the algebra of regular functions K[X] defined by the action of T is pointed, the group Aut(X) is a finite extension of T. As an application, we describe the automorphism group of a rigid trinomial affine hypersurface and find all isomorphisms between such hypersurfaces.