| I give a bound on which singularities may appear on KSBA stable surfaces for a wide range of topological invariants, and use this result to describe all stable numerical quintic surfaces, i.e. stable surfaces with K2= 5, pg=4, and q=0, whose unique non Du Val singularity is a Wahl singularity. Quintic surfaces are the simplest examples of surfaces of general type and the question of describing their moduli is a long-standing question in algebraic geometry. I then extend the deformation theory of Horikawa to the log setting in order to describe the boundary divisor of the moduli space of KSBA stable numerical quintic surfaces corresponding to these surfaces. |
