Семинар НУЛ АГП «Affine SL(2)-surfaces»

Let k be a field of characteristic zero and X be D//Z₂, where D is the Danielewski surface given by the equation 2xy-z² = 1. We plan to discuss and prove some properties of the smooth SL(2)-surface X. We will prove that SL(2)-action on X does not extend to four-dimensional affine space, however there exists an equivariant algebraic embedding of X into five-dimensional affine space. Besides, we will give a counter-example to the generalized Cancellation Problem using a construction with X and describe the automorphism group of X. The talk is based on (G. Freudenburg. A note on smooth affine SL(2)-surfaces. arXiv:2411.15879).