On the tautological rings of the moduli of K3 surfaces
-- Dragos Oprea, April 29, 2016

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I will discuss ongoing joint work with Alina Marian and Rahul
Pandharipande aimed at studying the tautological ring of the moduli
space of K3 surfaces. First, I will discuss the notion of tautological
classes. Next, I will explain a method of deriving relations between
tautological classes via the geometry of the relative Quot scheme. In
addition, the study of the Quot scheme of a fixed K3 surface leads to
a proof in the K3 case of a conjecture of M. Lehn regarding the top
Segre classes of tautological vector bundles over Hilbert schemes of
points.