Advisor(s)
Venkatraman Lakshmibai
Contributor(s)
Jerzy M. Weyman, Donald R. King, Pradeep Shukla
Date of Award
2009
Date Accepted
4-2009
Degree Grantor
Northeastern University
Degree Level
Ph.D.
Degree Name
Doctor of Philosophy
Department or Academic Unit
College of Arts and Sciences. Department of Mathematics.
Keywords
Algebraic geometry, Distributive lattice theory
Subject Categories
Toric varieties, Schubert varieties, Algebraic varieties, Geometry (Algebraic)
Disciplines
Mathematics
Abstract
This thesis has three distinct chapters: Bruhat-Hibi toric varieties, Gorenstein Schubert varieties in a minuscule G/P, and Wahl's conjecture for a minuscule G/P. We begin with a study of toric varieties associated to Bruhat lattices for a minuscule G/P. Our main result is a combinatorial characterization of the singular loci of these toric varieties. In the next chapter, we are concerned with Schubert varieties in a minuscule G/P, for which we give a combinatorial characterization for them to be arithmetically Gorenstein. In the last chapter, we prove Wahl's conjecture for a minuscule G/P.
Document Type
Dissertation
Rights Holder
Justin Allen Brown
Permanent URL
Recommended Citation
Brown, Justin Allen, "Some geometric properties of certain toric varieties and Schubert varieties" (2009). Mathematics Dissertations. Paper 6. http://hdl.handle.net/2047/d10018438
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