Jerzy M. Weyman, Donald R. King, Pradeep Shukla
Date of Award
Doctor of Philosophy
Department or Academic Unit
College of Arts and Sciences. Department of Mathematics.
Algebraic geometry, Distributive lattice theory
Toric varieties, Schubert varieties, Algebraic varieties, Geometry (Algebraic)
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.
Justin Allen Brown
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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