Structure of geometrically non-reduced varieties

Abstract

We prove a structural result for geometrically non-reduced varieties and give applications to Fano varieties. For example, we show that if $X$ is the generic fibre of a Mori fibre space of relative dimension $n$, and the characteristic is $p>2n+1$, then any geometric non-reducedness of $X$ comes from the base of some fibration.

31 pages. To appear in Trans. Amer. Math. Soc

References in corpus (1)

• On del Pezzo fibrations in positive characteristic

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