"HILBERT SCHEMES AND ENUMERATIVE GEOMETRY"
Prof. Dr. Claire Voisin
(Collège de France)
Thursday, July 11, 2019, 16:45h
Mathematikon, Hörsaal, Im Neuenheimer Feld 205
Consider an algebraic curve in 3-space; when projected generically to a plane, it will acquire a number of double points. This number depends only on the degree and the genus of the curve.
Computing similar numbers when the curve is replaced by a surface arbitrarily embedded will be the subject of the lecture. One key difference with the curve case is the fact that we have to work with the Hilbert
scheme of k points, instead of the k-th symmetric product, and I will spend some time on the construction of the Hilbert scheme. The main result I will present is the Lehn conjecture, now a theorem, computing
all these numbers for all surfaces in terms of their numerical (complex cobordism) invariants