Segre Classes of Tautological Bundles on Hilbert schemes of Points
Time: 2016-10-25
Published By: Ningbo Lu
Speaker(s): Zhilan Wang （AMSS）
Time: 15:15-17:15 September 29, 2016
Venue: Room 9, Quan Zhai, BICMR
Abstract. We focus on computations of Segre classes of tautological
bundles on Hilbert schemes of points of $X$, which are related to
questions of enumerative geometry.
When $X$ is
a surface, Lehn made a conjecture on the closed formula of such numbers
in 1999. And in 2015 Marian, Oprea and Pandharipande proved Lehn's
conjecture for K3 surfaces using localization on the Quot schemes of X.
In this talk I will briefly review their proof.
When
$X$ is a curve, the Hilbert scheme of $n$ points is isomorphic to the
$n$-th symmetric product of $X$, and the generating series of such
numbers are obtained by Le Barz, Cotterill using different methods. In
this talk we will explain how localization method are applied to derive
such generating series.
