Back to Algebraic Geometry Seminar: Fall 2012
Algebraic Geometry Seminar
Date: Tuesday, Nov 6, 2012
Time: 3:30PM - 4:30PM
Location: JTB 120
Colleen Robles
Texas A&M University
Title |
Homological flexibility of Schubert classes in cominuscule rational homogeneous varieties |
Abstract |
The Schubert subvarieties of a rational homogeneous variety X are distinguished by the fact that their homology classes form an additive basis of the integer homology of X. It is then natural to ask: does a Schubert classes admit any other algebraic representatives (aside from the Schubert variety)? It is a remarkable consequence of Kostant’s work on Lie algebra homology that, in the the case that X is cominuscule – equivalently, X admits the structure of a compact Hermitian symmetric space (eg. X is a complex Grassmannian) – the algebraic representatives of a Schubert class are solutions of a system of differential equations. This allows us to apply differential geometric techniques to the problem. I will discuss this, and related questions, and the essential role played by representation theory in determining both rigidity (the Schubert varieties are the only algebraic representatives) and flexibility. |
Algebraic Geometry