Veronika Kikteva to speak on 'Presentations, Embeddings and Automorphisms of Homogeneous Spaces for SL_2(k)'

On November 26, 2025, Veronika Kikteva, Research Assistant at the Laboratory on Algebraic Transformation Groups, will speak on 'Presentations, Embeddings and Automorphisms of Homogeneous Spaces for SL_2(k)'.

Abstract:

Let k be an algebraically closed field of characteristic zero and G be a linear algebraic k-group. It is well known that every affine G-variety admits a G-equivariant closed embedding into a finite-dimensional G-module. Such an embedding is a presentation of the G-variety, and a presentation is called minimal if the dimension of the corresponding G-module is minimal. The problem of finding a minimal presentation generalizes the problem of determining whether a group action on affine space is linearizable.

We discuss a minimal presentation for each homogeneous space of SL2(k). Of particular interest are the surfaces Y = SL2(k)/T and X = SL2(k)/N, where T is the one-dimensional torus and N is its normalizer. 

In the previous talk, it was shown that the minimal presentation of X has dimension 5, while the embedding dimension of X is 4, and there exists no closed SL2(k)-equivariant embedding of X into A4. Thus, the SL2(k)-action on X is absolutely nonextendable to A4. In addition, X is noncancelative, that is, there exists a surface X' such that X x A1 is isomorphic to X' x A1 and X is not isomorphic to X'. We consider two other examples of surfaces with absolutely nonextendable group actions. 

This talk is based on the work [Gene Freudenburg. Presentations, embeddings and automorphisms of homogeneous spaces for SL2(C). arXiv:2504.21712].

Start time: 18:00

Venue: 11 Pokrovsky Bulvar, Room M203