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.
Citation
Caucher Birkar. "On connectedness of non-klt loci of singularities of pairs." J. Differential Geom. 126 (2) 431 - 474, February 2024. https://doi.org/10.4310/jdg/1712344217
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