On the affineness of Deligne-Lusztig varieties

TL;DR

This paper proves that Deligne-Lusztig varieties linked to minimal length elements in any $ ext{d}$-conjugacy class of the Weyl group are affine, confirming a conjecture by Orlik and Rapoport.

Contribution

It establishes the affineness of these Deligne-Lusztig varieties, resolving a conjecture in the field.

Findings

Proves affineness of Deligne-Lusztig varieties for minimal length elements.

Confirms a conjecture by Orlik and Rapoport.

Advances understanding of the geometric properties of these varieties.

Abstract

We prove that the Deligne-Lusztig variety associated to minimal length elements in any $\d$-conjugacy class of the Weyl group is affine, which was conjectured by Orlik and Rapoport in \cite{OR}.