Open surfaces with a triangle at infinity

Dmitriy Chunaev; Alexander Perepechko; Daniil Shunin

Open surfaces with a triangle at infinity

Algebraic Geometry 2026-07-15 v1

Authors: Dmitriy Chunaev , Alexander Perepechko , Daniil Shunin

Abstract

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.

Cite

@article{arxiv.2607.14055,
  title  = {Open surfaces with a triangle at infinity},
  author = {Dmitriy Chunaev and Alexander Perepechko and Daniil Shunin},
  journal= {arXiv preprint arXiv:2607.14055},
  year   = {2026}
}