Open surfaces with a triangle at infinity
arXiv:2607.14055
summary
The paper classifies open algebraic surfaces whose compactifications contain a triangle of contractible (‑1)-curves, shows these affine surfaces coincide with cubic surfaces of Markov type, and describes their automorphism groups.
Abstract
A triangle surface is an open algebraic surface completed by a triangle of contractible -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.
Topics & keywords
#open algebraic surfaces#triangle surfaces#contractible -1 curves#cubic surfaces#Markov type#automorphism groups-1 curvesaffine triangle surfaceMarkov cubiccombinatorial classificationautomorphism group