Standard stable Horikawa surfaces

Abstract

In 1976 Horikawa classified minimal surfaces of general type with $K_X^2 = 2p_g(X)-4$, the equality case of Noether's inequality. If $K_X^2$ is divisible by 16, then there are two irreducible families and it is along-standing open problem if these parametrise diffemorphic surfaces. Considering these surfaces inside the moduli space of stable surfaces, I will construct an anticipated intersection of the two components and some unexpected extra components.
The talk is based on joint work with Julie Rana.

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