Date of Award
9-2010
Document type
dissertation
Access Type
Open Access Dissertation
Degree Name
Doctor of Philosophy (PhD)
Degree Program
Mathematics
First Advisor
Paul E. Gunnells
Second Advisor
Tom Braden
Third Advisor
David Kastor
Subject Categories
Mathematics | Statistics and Probability
Abstract
In [JM02, section 14], Ji and MacPherson give new constructions of the Borel--Serre and reductive Borel--Serre compactifications [BS73, Zuc82] of a locally symmetric space. They use equivalence classes of eventually distance minimizing (EDM) rays to describe the boundaries of these compactications. The primary goal of this thesis is to construct the Satake compactifications of a locally symmetric space [Sat60a] using finer equivalence relations on EDM rays. To do this, we first construct the Satake compactifications of the global symmetric space [Sat60b] with equivalence classes of geodesics in the symmetric space. We then define equivalence relations on EDM rays using geometric properties of their lifts in the symmetric space. We show these equivalence classes are in one-to-one correspondence with the points of the Satake boundary. As a secondary goal, we outline the construction of the toroidal compactifications of Hilbert modular varieties [Hir71, Ehl75] using a larger class of "toric curves" and equivalence relations that depend on the compactications' defining combinatorial data.
DOI
https://doi.org/10.7275/1667590
Recommended Citation
Boland, Patrick Michael, "Geometry of Satake and Toroidal Compactifications" (2010). Open Access Dissertations. 270.
https://doi.org/10.7275/1667590
https://scholarworks.umass.edu/open_access_dissertations/270