Semi-positivity in positive characteristics

DOI10.24033/ASENS.2232zbMATH Open1326.14015arXiv1208.5391OpenAlexW2267204329MaRDI QIDQ2938669

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Publication date: 14 January 2015

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Abstract: Let $f:(X,Delta)oY$ be a flat, projective family of sharply $F$-pure, log-canonically polarized pairs over an algebraically closed field of characteristic $p>0$ such that $pmidind(K_{X/Y}+Delta)$. We show that $K_{X/Y}+Delta$ is nef and that $f_{*}(s{O}_X(m(K_{X/Y}+Delta)))$ is a nef vector bundle for $mgg0$ and divisible enough. Some of the results also extend to non log-canonically polarized pairs. The main motivation of the above results is projectivity of proper subspaces of the moduli space of stable pairs in positive characteristics. Other applications are Kodaira vanishing free, algebraic proofs of corresponding positivity results in characteristic zero, and special cases of subadditivity of Kodaira-dimension in positive characteristics.

Full work available at URL: https://arxiv.org/abs/1208.5391

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