On connectedness of non-klt loci of singularities of pairs

Caucher Birkar

Algebraic Geometry mathscidoc:2210.45001

2022.5
We study the non-klt locus of singularities of pairs. We show that given a pair (X, B) and a projective morphism X → Z with connected fibres such that −(KX +B) is nef over Z, the non-klt locus of (X, B) has at most two connected components near each fibre of X → 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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@inproceedings{caucher2022on,
  title={On connectedness of non-klt loci of singularities of pairs},
  author={Caucher Birkar},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20221007153623868888730},
  year={2022},
}
Caucher Birkar. On connectedness of non-klt loci of singularities of pairs. 2022. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20221007153623868888730.
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