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arXiv · 2010.08226

On connectedness of non-klt loci of singularities of pairs

Caucher Birkar
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Abstract

We study the non-klt locus of singularities of pairs. We show that given a pair $(X,B)$ and a projective morphism $X\to Z$ with connected fibres such that $-(K_X+B)$ is nef over $Z$, the non-klt locus of $(X,B)$ has at most two connected components near each fibre of $X\to Z$. This was conjectured by Hacon and Han. In a different direction we answer a question of Mark Gross on connectedness of the non-klt loci of certain pairs. This is motivated by constructions in Mirror Symmetry.

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Caucher Birkar. 2020-10-16. On connectedness of non-klt loci of singularities of pairs. https://arxiv.org/abs/2010.08226

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