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arXiv · 2403.01154

Boundedness of klt complements on Fano fibrations over surfaces

Bingyi Chen
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Abstract

Let $(X,B)$ be an $\epsilon$-lc pair of dimension $d$ with a closed point $x\in X$. Birkar and Shokurov conjectured that there is an effective Cartier divisor $H$ passing through $x$ such that $(X,B+tH)$ is lc near $x$, where $t$ is a positive real number depending only on $d,\epsilon$. We prove that this conjecture is equivalent to Shokurov's conjecture on boundedness of klt complements on Fano fibrations and we confirm it in dimension 2. As a corollary, we prove the boundedness of klt complements on Fano fibrations over surfaces.

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Bingyi Chen. 2024-03-02. Boundedness of klt complements on Fano fibrations over surfaces. https://arxiv.org/abs/2403.01154

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