Hyper-Kaehler fibrations and Hilbert schemes

• Main Author: Kamenova, Ljudmila K
• Other Authors: Gang Tian.
• Format: Others
• Language: English
• Published: Massachusetts Institute of Technology 2006
• Subjects: Mathematics.
• Online Access: http://hdl.handle.net/1721.1/34686

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.