Additive actions and local algebras: the Hassett-Tschinkel correspondence

Time: 9:30 - 10:30, October 28, 2026

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

Abstract: An additive action on an algebraic variety X is an effective regular action of the vector group (K^n,+) with an open orbit. In 1999, Hassett and Tschinkel established a correspondence between additive actions on projective spaces and artinian local commutative associative algebras with units. This correspondence can be generalized to describe induced additive actions on projective hypersurfaces. In particular, additive actions on non-degenerate hypersurfaces correspond to Gorenstein local algebras. We will discuss further connections between the geometry of additive actions and the properties of the corresponding algebras, talk about the problem of classifying low‑dimensional algebras, and formulate some open problems. The talk is based on results of the project “International Academic Cooperation” HSE University.