Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

Compactification of a Drinfeld period domain over a finite field


Authors: Richard Pink and Simon Schieder
Journal: J. Algebraic Geom. 23 (2014), 201-243
DOI: https://doi.org/10.1090/S1056-3911-2013-00605-0
Published electronically: October 17, 2013
MathSciNet review: 3166390
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Abstract | References | Additional Information

Abstract: 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  $ \geqslant 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.


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Additional Information

Richard Pink
Affiliation: Department of Mathematics, ETH Zürich, 8092 Zürich, Switzerland
Email: pink@math.ethz.ch

Simon Schieder
Affiliation: Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138
Email: schieder@math.harvard.edu

DOI: https://doi.org/10.1090/S1056-3911-2013-00605-0
Received by editor(s): January 26, 2011
Received by editor(s) in revised form: June 7, 2011
Published electronically: October 17, 2013
Additional Notes: The second author was supported by the International Fulbright Science and Technology Award of the U.S. Department of State
Article copyright: © Copyright 2013 University Press, Inc.
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society