Hyper-Kaehler fibrations and Hilbert schemes

Hyper-Kaehler fibrations and Hilbert schemes

Alternative Title: Hyper-Kähler fibrations and Hilbert schemes

Author: Kamenova, Ljudmila K

Citable URI: http://hdl.handle.net/1721.1/34686

Other Contributors: Massachusetts Institute of Technology. Dept. of Mathematics.

Advisor: Gang Tian.

Department: Massachusetts Institute of Technology. Dept. of Mathematics.

Publisher: Massachusetts Institute of Technology

Date Issued: 2006

Abstract:

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.

Description:

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).

URI: http://hdl.handle.net/1721.1/34686

Keywords: Mathematics.

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