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

· 2017 · math.AG · arXiv 1710.03818

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abstract

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 · 2025-01-02 · conditional · novelty 8.0

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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  • Pathological MMP singularities as $\alpha_p$-quotients math.AG · 2025-01-02 · conditional · none · ref 5 · internal anchor

    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.