On the projectivity of the moduli space of stable surfaces in characteristic p>5

Zsolt Patakfalvi

On the projectivity of the moduli space of stable surfaces in characteristic p>5

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arxiv 1710.03818 v3 pith:2MLZQG4B submitted 2017-10-10 math.AG

Zsolt Patakfalvi This is my paper · ORCID

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keywords modulispacecharacteristicprojectivestablesurfacesalgebraicallyclosed

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We prove that every proper subspace of the moduli space of stable surfaces with fixed volume over an algebraically closed field of characteristic p>5 is projective. As a consequence we also deduce that the same moduli space is projective over Z[1/30] modulo two conjectural local properties of the moduli functor.

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Pathological MMP singularities as $\alpha_p$-quotients
math.AG 2025-01 conditional novelty 8.0 of 10

For every positive characteristic, the author constructs non-S3 terminal singularities of dimension p+1 and stable families with klt, Cohen-Macaulay, F-injective general fibers but non-S2 special fibers.

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