Some geometric properties of certain toric varieties and schubert varieties

• Online Access: http://hdl.handle.net/2047/d10018438

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.