The motive of the Hilbert scheme of points in all dimensions – Michele Graffeo (SISSA, Trieste)
mercoledì 16 ott 2024 1:00 PM — 2:00 PM Aula Seminari (Department of Mathematics) Seminars, Algebraic and Arithmetic Geometry Seminar
The Hilbert scheme of points on a quasi-projective variety is a classical object in algebraic geometry. However, its geometry is nowadays still not completely accessible. On the other hand, the motive of a variety is an invariant attached to carrying a lot of information about its geometry, and it is considered as a universal Euler characteristic. In a joint project with Monavari, Moschetti and Ricolfi we give general formulas to compute the motive of the Hilbert scheme of points, provided the knowledge of a finite amount of data (that we gave explicitly in some cases). In my seminar I will present our formulas and I will show many applications.