Compactification des vari\'et\'es de Deligne-Lusztig

TL;DR

This paper explicitly constructs the normalization of the Bott-Samelson-Demazure-Hansen compactification of Deligne-Lusztig varieties, providing insights into their local monodromy properties around divisors.

Contribution

It offers an explicit construction of the normalization of a key compactification of Deligne-Lusztig varieties, clarifying their local monodromy behavior.

Findings

Explicit normalization of the compactification constructed.

Retrieval of Deligne-Lusztig's local monodromy result.

Enhanced understanding of the geometry of Deligne-Lusztig varieties.

Abstract

We 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.