Riley Burton: Triangle Singularities

In [Loo84], Looijenga carried out the study of the deformation theory of his Fuchsian singularities: certain normal affine surface singularities admitting a good ℂ*-action. In this talk, we will take a detailed look at perhaps the simplest class of Fuchsian singularity, the triangle singularities. In particular, we will introduce what these are through an explicit example, and describe their deformations. Along the way, we will see that triangle singularities are tightly connected with K3 surfaces that contain a so-called “T_p, q, r-curve”. We will describe these K3 surfaces and explore this connection in detail.

[Loo84] Eduard Looijenga. The smoothing components of a triangle singularity. II. Math. Ann., 269(3):357–387, 1984.