2010/07/27 by Richard Pink, Pink, Richard, Simon Schieder +1
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic and geometric function theory #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1007.4796
openalex publication_date 2010/07/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a certain compactification of the Drinfeld period domain over a finite field which arises naturally in the context of Drinfeld moduli spaces. Its boundary is a disjoint union of period domains of smaller rank, but these are glued together in a way that is dual to how they are glued in the compactification by projective space. This compactification is normal and singular along all boundary strata of codimension ≥2. We study its geometry from various angles including the projective coordinate ring with its Hilbert function, the cohomology of twisting sheaves, the dualizing sheaf, and give a modular interpretation for it. We construct a natural desingularization which is smooth projective and whose boundary is a divisor with normal crossings. We also study its quotients by certain finite groups.