Hyper-Kähler fibrations and Hilbert schemes

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2006.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 41-42).In this thesis, I consider hyper-Kähler manifolds of complex dimension 4 which are fibrations. It is known that the fibers are abelian varieties and the base is P2. We assume that the general fiber is isomorphic to a product of two elliptic curves. We are able to relate this class of hyper-Kähler fibrations to already known examples. We prove that such a hyper-Kähler manifold is deformation equivalent to a Hilbert scheme of two points on a K3 surface.by Ljudmila K. Kamenova.Ph.D