2018/04/18 by Georg Linden, Linden, Georg
Mathematics · #14G15 (Primary) 14M27 (Secondary) #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research
paper · pdf · doi:10.48550/arxiv.1804.06722
openalex publication_date 2018/04/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
When considered as a Deligne-Lusztig variety, the Drinfeld half space ΩV over a finite field k has a compactification whose boundary divisor is normal crossing and which can be obtained by successively blowing-up projective space along linear subspaces. Pink and Schieder (2014) have introduced a new compactification of ΩV whose strata of the boundary are glued together in a way dual to the way they are for the tautological compactification by projective space. We show that by applying an analogous sequence of blow-ups to this new compactification we arrive at the compactification by Deligne and Lusztig as well. Moreover, we compute for each of these three compactifications the stabilizers of k-valued points under the canonical PGL(V)-action. We find that in each case the stratification can be recovered from the unipotent radicals of these stabilizers.