Deformations of Hilbert Schemes of Points on K3 Surfaces and Representation Theory
Hassett, Brendan E.
Doctor of Philosophy
We study the cohomology rings of Kaehler deformations X of Hilbert schemes of points on K3 surfaces by representation theory. We compute the graded character formula of the Mumford - Tate group representation on the cohomology ring of X. Furthermore, we also study the Hodge structure of X, and find the generating series for deducting the number of canaonical Hodge classes in the middle cohomology.
Hilbert scheme; Representation theory; Hyperkaehler manifolds