Algebraic Geometry Seminar Fall 2011
The seminar meets on Fridays at 2:25 pm in Van Vleck B215.
The schedule for the previous semester is here.
|Sep. 23||Yifeng Liu (Columbia)||Arithmetic inner product formula||Tonghai Yang|
|Oct. 7||Zhiwei Yun (MIT)||Cohomology of Hilbert schemes of singular curves|
|Oct. 14||Javier Fernández de Bobadilla (Instituto de Ciencias Matematicas, Madrid)||Nash problem for surfaces|
|Nov. 25||Shamgar Gurevich (Madison)||Canonical Hilbert Space: Why? How? and its Categorification|
|May 4||Mark Andrea de Cataldo (Stony Brook)||TBA||Maxim|
Cohomology of Hilbert schemes of singular curves
Abstract: For a smooth curve, the Hilbert schemes are just symmetric powers of the curve, and their cohomology is easily computed by the H^1 of the curve. This is known as Macdonald's formula. In joint work with Davesh Maulik, we generalize this formula to curves with planar singularities (which was conjectured by L.Migliorini). In the singular case, the compactified Jacobian will play an important role in the formula, and we make use of Ngo's technique in his celebrated proof of the fundamental lemma.