Time: 9h30 – 11h00, Wednesday October 16, 2024

Venue: Room 612, A6, Institute of Mathematics-VAST

Abstract: This is based on a joint work with Mikhail Petrov. A trinomial variety is an affine irreducible variety defined by a system of trinomial equations of special form. The coordinates are divided onto groups, and for each group, a monomial in the variables in this group is fixed. Each equation consists of three such monomials. In 2017, J. Hausen and M. Wrobel proved that each variety with a torus action of complexity one, satisfying certain conditions, can be obtained from a trinomial variety via Cox's construction.

We are interested in computing the Makar-Limanov invariant of trinomial varieties. Recall that the Makar-Limanov invariant is the intersection of all kernels of locally nilpotent derivations, or equivalently, the invariant subalgebra for all algebraic actions of the additive group of the ground field. If it coincides with the ring of regular functions, the variety is called rigid. In general, computing the Makar-Limanov invariant of a trinomial variety is a challenging problem. However, we prove that a cylinder over a non-rigid trinomial variety has a trivial Makar-Limanov invariant.

Program of Special Semester on Commutative Algebra