ИСТИНА

Trinomial variety is an affine algebraic variety given by a system of trinomial equations. This class of varieties is interesting since each rational normal affine variety with a torus action of complexity one can be obtained as a good quotient of a trinomial variety by an action of quasitorus. Moreover this is the Cox realization of this variety. In the talk we prove the criterion of rigidity of a trinomial variety and describe the automorphism group of a rigid trinomial variety and obtain some partial results about Makar-Limanov invariant of such varieties. Also we apply Bhatwadekar's technique to compute stable Makar-Limanov invariant of trinomial varieties. This talk is based on a joint works with Polina Evdokimova, Anton Shafarevich, Viktoriia Borovik, and Mikhail Petrov.