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arXiv · 2011.10226

Invariance of plurigenera fails in positive and mixed characteristic

Iacopo Brivio
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Abstract

We construct smooth families of elliptic surface pairs with terminal singularities over a DVR of positive or mixed characteristic $(X,B)\to \mathrm{Spec}R$, such that $P_m(X_k,B_k)>P_m(X_K,B_K)$ for all sufficiently divisible $m>0$. In particular, this shows that invariance of all sufficiently divisible plurigenera does not follow from the MMP and Abundance Conjectures.

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Iacopo Brivio. 2020-11-20. Invariance of plurigenera fails in positive and mixed characteristic. https://arxiv.org/abs/2011.10226

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