“Nilpotent varieties: properties of the most classical cases”
Giovedì 20 Febbraio 2020, ore 11:30 - Aula 2BC30 - Abraham Broer (Università di Montreal)
This is the first of hopefully several lectures on nilpotent varieties. Nilpotent varieties are quasi-homogeneous varieties for a complex reductive group, that contain a dense orbit locally isomorphic to an orbit of nilpotent elements in the Lie algebra of the group. For example a finite cover of an orbit closure in the Lie algebra, or the cotangent bundle of any complete homogeneous variety.
I have sought to generalize properties, mostly well-known, of the most classical cases of the full nilpotent cone and the closely related cotangent bundle of the full flag variety of the group. In later lectures I hope to expose some of these newer results. So I think it makes sense to start by recalling (or introducing) some of these classical properties: touching on normality, invariant theory and exponents of hyperplane arrangements, the class group of the variety related to the Cartan matrix, cohomology of line bundles, calculating global sections, formulating higher vanishing theorems and rational singularities.