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Julie Rana : Moduli of general type surfaces

It has been 30 years since Koll\’ar and Shepherd-Barron published their groundbreaking paper describing a compactification of Gieseker’s moduli space of surfaces of general type. As with all compactifications, the work raised natural questions. What is the structure of these moduli spaces and the boundary in particular? What sorts of singularities might we expect to obtain? What types of surfaces give rise to divisors in the moduli space, and are these divisors smooth? We discuss general results bounding types of Wahl singularities, and use them to address these questions in the context of Horikawa-type surfaces.

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