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arXiv · 1708.04268

Singularities of General Fibers and the LMMP

Zsolt Patakfalvi·Joe Waldron
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Abstract

We use the theory of foliations to study the relative canonical divisor of a normalized inseparable base-change. Our main technical theorem states that it is linearly equivalent to a divisor with positive integer coefficients divisible by $p-1$. We deduce many consequences about the fibrations of the minimal model program: for example the general fibers of terminal $3$-fold Mori fiber spaces are normal in characteristic $p\geq 5$ and smooth in characteristic $p\geq 11$.

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Zsolt Patakfalvi, Joe Waldron. 2017-08-14. Singularities of General Fibers and the LMMP. https://arxiv.org/abs/1708.04268

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