Makoto Enokizono, Normal stable degenerations of Noether-Horikawa surfaces

Noether-Horikawa surfaces are surfaces of general type satisfying the equation K²=2p_g−4, which represents the equality of the Noether inequality K²≥2p_g−4 for surfaces of general type. In the 1970s, Horikawa conducted a detailed study of smooth Noether-Horikawa surfaces, providing a classification of these surfaces and describing their moduli spaces.
In this talk, I will present an explicit classification of normal stable degenerations of Noether-Horikawa surfaces. Specifically, I will discuss the following results:
(1) Classification of Noether-Horikawa surfaces with Q-Gorenstein smoothable log canonical singularities.
(2) Criterion for determining the (global) Q-Gorenstein smoothability of the surfaces described in (1).
(3) Description of the KSBA moduli spaces for Q-Gorenstein smoothable normal stable Noether-Horikawa surfaces.
This is joint work with Hiroto Akaike, Masafumi Hattori and Yuki Koto.