Algebraic Surfaces
and Their Singularities

The workshop is devoted to algebraic surfaces and singularity theory. Its purpose is to facilitate scholarly exchange and collaboration among experts in these areas. 

Titles and Abstracts

• Marcos Canedo _ Pontificia Universidad Católica de Chile

  • • Classification of Small surfaces with only WQHD singularities
      A $\mathbb{Q}$HD singularity is a normal two-dimensional singularity that admits a smoothing with Milnor number equal to zero. Wahl conjectured that every $\mathbb{Q}$HD singularity is weighted homogeneous, and their classification was done by Bhupal and Stipsicz. We refer to them as W$\mathbb{Q}$HD singularities. (They are typically non-log-canonical; the log-canonical ones are Wahl singularities and three quotients of certain elliptic singularities.) On the other hand, small surfaces arise naturally in the classification of W$\mathbb{Q}$HD surfaces on the Noether line $K^2 = 2p_g - 4$. In this talk, we will introduce small surfaces and establish an inequality that allows us to show that W$\mathbb{Q}$HD surfaces on the Noether line must be small. If time permits, we will also discuss progress toward a classification of small surfaces with only W$\mathbb{Q}$HD singularities. This is a joint work with Giancarlo Urzúa.

• DongSeon Hwang _ IBS  Center for Complex Geometry

• Jaekwan Jeon _ IBS Center for Geometry and Physics

• Giancarlo Urzúa _ Pontificia Universidad Católica de Chile

  • • Classification of T-surfaces with $K^2 \le 2p_g-3$
      I will explain the techniques and results of a recent and ongoing work together with Vicente Monreal and Jaime Negrete which classifies surfaces with only T-singularities and $K^2 \le 2p_g-3$. This includes non-smoothable surfaces with $K^2 < 2p_g-4$, Horikawa surfaces $K^2=2p_g-4$, and Horikawa surfaces on the Noether line plus 1, this is, $K^2=2p_g-3$. The latter includes I-surfaces and quintics.

• Yoonjeong Yang _ Chungnam National University

  • • Numerical Godeaux surfaces with $H_1=\mathbb{Z}/4\mathbb{Z}$
      We construct minimal complex surfaces of general type with invariants $K^2=1$ and $p_g=q=0$ as double covers of Enriques surfaces. The main example comes from the seven--nodal Enriques surface studied by Mukai and by Ito--Ohashi; a second example uses Kondo's fifth Enriques surface. In particular,  $H_1(S,\mathbb{Z})=\mathbb{Z}/4\mathbb{Z}$ for the first example $S$.

Timetable

2025-10-31 (Friday)

• 10:00--11:00: DongSeon Hwang

• 11:30--12:30: Marcos Canedo

• 12:30--14:00: Lunch

• 14:00--15:00: Jaekwan Jeon

• 15:30--16:30: Yoonjeong Yang

• 17:00--18:00: Giancarlo Urzúa

• 18:00--20:00: Banquet