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.
@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.