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Boundary Divisors In The Moduli Space Of Stable Quintic Surfaces, Julie Rana

Doctoral Dissertations

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 K^2= 5, p_g=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 …