K_{X/T} is pseudo-effective when f: X→T has non-uniruled generic fiber in char p>0.
Singularities of General Fibers and the LMMP
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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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2020 1verdicts
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Pseudo-effectivity of the relative canonical divisor and uniruledness in positive characteristic
K_{X/T} is pseudo-effective when f: X→T has non-uniruled generic fiber in char p>0.