Chennai Mathematical Institute


Generic Fiber of the Springer fiber of type A
Dr. Pagnon Ngoc Gioan Jean
ICTP, Trieste, Italy.


It is well-known that when the Lie algebra is of type $A,D,E$ the Springer fiber [set of (complete) flags fixed by a nilpotent element] above a subregular nilpotent element is described by the Dynkin diagram and is called the Dynkin curve of the Lie algebra. On the other hand the closure of the minimal nilpotent orbit for a Lie algebra of type A, is obtained by collapsing the zero section of a cotangent bundle of a projective space ${\mathbb{P}}^{k}$. In this lecture, I will give give this generalization for the generalized Springer resolution of type $A$ which is a desingularization of the closure of an nilpotent orbit, by giving a complete description of the generalized Springer fiber above a generic singularities showing that it is isomorphic to a Dynkin curve or to a projective space.