2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/168250We construct explicitly the normalisation of the Bott-Samelson-Demazure-Hansen compactification of Deligne-Lusztig varieties $X(w)$ in their covering $Y(w)$: we retrieve a result by Deligne-Lusztig about the local monodromy around the divisors of the compactification.14 pages. Minor correctionsAlgebraic GeometryGroup Theorytext