Seminar 'Equivariant Embeddings of the Heisenberg Group into Projective Space'

On January 14, 2026, Anton Shafarevich, Research Fellow at the Laboratory on Algebraic Transformation Groups, will speak on the 'Equivariant Embeddings of the Heisenberg Group into Projective Space'.

Abstract:

Let G be a connected linear algebraic group. An equivariant embedding of the group G into an algebraic variety X is an open embedding of G into X such that the action of G on itself by left translations extends to an action of G on X. For example, equivariant embeddings of an algebraic torus are described by the theory of toric varieties. Equivariant embeddings of the group SL2(С) into affine algebraic varieties were described by V. Popov.

Equivariant embeddings of the vector group (Ga)n into projective space Pn were described by F. Knop and H. Lange, and independently by B. Hassett and Yu. Tschinkel. In particular, their results imply that for n > 6 there exist infinitely many pairwise inequivalent embeddings of (Ga)n into Pn.

The closest analogue of the group (Ga)n is the Heisenberg group. It is also a unipotent group, and its commutator subgroup is one-dimensional. Following the work of Cong Ding and Zhijun Luo, we will show that the Heisenberg group admits infinitely many equivariant embeddings into projective space.

Start time: 18:00

Venue: 11 Pokrovsky Bulvar