arXiv subjects
Publications and source records attributed to Daniil Shunin.
A triangle surface is an open algebraic surface completed by a triangle of contractible $(-1)$-curves. We establish a combinatorial description of their completions. We also show that affine triangle surfaces are exactly cubic surfaces of Markov type. Explicit description of their automorphism groups is provided.
Dual representations $V$ and $V^*$ of a complex connected algebraic group $G$ simultaneously have either infinitely or finitely many orbits. Whenever the latter holds, the orbits in $V$ and $V^*$ are in a bijective correspondence called Pyasetskii duality. We obtain a complete description of this duality in the case of spherical representations.