Arithmetic and geometric deformations of -pure and -regular singularities
K Sato, S Takagi - arXiv preprint arXiv:2103.03721, 2021 - arxiv.org
K Sato, S Takagi
arXiv preprint arXiv:2103.03721, 2021•arxiv.orgGiven a normal $\mathbb {Q} $-Gorenstein complex variety $ X $, we prove that if one
spreads it out to a normal $\mathbb {Q} $-Gorenstein scheme $\mathcal {X} $ of mixed
characteristic whose reduction $\mathcal {X} _p $ modulo $ p $ has normal $ F $-pure
singularities for a single prime $ p $, then $ X $ has log canonical singularities. In addition,
we show its analog for log terminal singularities, without assuming that $\mathcal {X} $ is
$\mathbb {Q} $-Gorenstein, which is a generalization of a result of Ma-Schwede. We also …
spreads it out to a normal $\mathbb {Q} $-Gorenstein scheme $\mathcal {X} $ of mixed
characteristic whose reduction $\mathcal {X} _p $ modulo $ p $ has normal $ F $-pure
singularities for a single prime $ p $, then $ X $ has log canonical singularities. In addition,
we show its analog for log terminal singularities, without assuming that $\mathcal {X} $ is
$\mathbb {Q} $-Gorenstein, which is a generalization of a result of Ma-Schwede. We also …
Given a normal -Gorenstein complex variety , we prove that if one spreads it out to a normal -Gorenstein scheme of mixed characteristic whose reduction modulo has normal -pure singularities for a single prime , then has log canonical singularities. In addition, we show its analog for log terminal singularities, without assuming that is -Gorenstein, which is a generalization of a result of Ma-Schwede. We also prove that two-dimensional strongly -regular singularities are stable under equal characteristic deformations. Our results give an affirmative answer to a conjecture of Liedtke-Martin-Matsumoto on deformations of linearly reductive quotient singularities.
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