Explicit KSBA compactifications of moduli spaces of secondary and tertiary Burniat surfaces

Valery Alexeev; Xiaoyan Hu

Explicit KSBA compactifications of moduli spaces of secondary and tertiary Burniat surfaces

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arxiv 2309.11397 v2 pith:745I6KCJ submitted 2023-09-20 math.AG

Valery Alexeev , Xiaoyan Hu This is my paper · ORCID

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keywords surfacesburniatcompactificationsksbamodulispacesaddingample

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abstract

We describe explicitly the geometric KSBA compactifications, obtained by adding slc surfaces~$X$ with ample canonical class, of moduli spaces of Burniat surfaces of degrees $K^2=5$, $4$ and $3$.

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Every Q-Gorenstein smoothable normal stable Horikawa surface falls into one of seven explicit families, and its global smoothability is controlled by a single local condition at its elliptic double cone singularities.

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