LOCAL SIMPLE CONNECTEDNESS OF RESOLUTIONS OF LOG-TERMINAL SINGULARITIES

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Polarized endomorphisms of complex normal varieties (2009, unknown): “Here, π1(Ỹ ) ≃ π1(Y ) by [52] since Y has only quotient singularities.”
The dual complex of Calabi–Yau pairs (2015, unknown): “5] in the algebraic case and [35] in general.”
Building blocks of étale endomorphisms of complex projective manifolds (2009, background): “5], and is in fact a π1-rational singularity from [51].”
Boundary complexes and weight filtrations (2011, background): “ies that are general with respect to their Newton polyhedra. By work of Takayama on fundamental groups of exceptional divisors, resolution complexes of log terminal singularities are simply connected [Tak03], but it is not known whether they are contractible. Here we give an example of an isolated r”
Codimension 1 foliations with numerically trivial canonical class on singular spaces (2018, background): “.3, suppose in addition that Xhas klt singularities. Suppose that β−1G is given by a closed rational 1-form ω Zwith values in a ﬂat line bundle LZwhose zero set has codimension at least two. Applying [Tak03], we see that there exists a ﬂat line bundle LX on Xsuch that LZ ∼= β∗LX. Then ωZ induces a c”
The local fundamental group of a Kawamata log terminal singularity is finite (2020, background): “The proof in [53] is similar to that of [56], but the latter manages to avoid the L2-index theorem, which turns out to be very important to us.”