Abundance for threefolds in positive characteristic when $\nu=2$

Zheng Xu

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arXiv · 2307.03938

Abundance for threefolds in positive characteristic when $\nu=2$

Zheng Xu

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Abstract

In this paper, we prove the abundance conjecture for threefolds over a perfect field $k$ of characteristic $p > 3$ in the case of numerical dimension equals to $2$. More precisely, we prove that if $(X,B)$ be a projective lc threefold pair over $k$ such that $K_{X}+B$ is nef and $\nu(K_{X}+B)=2$, then $K_{X}+B$ is semiample.

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Zheng Xu. 2023-07-08. Abundance for threefolds in positive characteristic when $\nu=2$. https://arxiv.org/abs/2307.03938

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