Working Seminar on

Complex and Algebraic Geometry:

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The Mumford-Horrocks Bundle

Dr. Avery Ching

HKUST, Hong Kong

Abstract

We will study an example of an indecomposable rank two vector bundle on the four dimensional projective space. Indeed, the only known example is an extension of the normal bundle of an abelian surface, which is known as the Mumford-Horrocks bundle. In the first lecture, we will review the basic stuff about line bundles over an abelian variety, including a description of their chern classes, theta functions and Heisenberg groups. These are all important tools to study the rational map given by a line bundle.

In the second lecture, we will work on the particular case in which an Abelian surface is imbedded into the four dimensional projective space. The Mumford-Horrocks bundle is then obtained as a direct consequence of it.

Lectuee 2:	July 5, 2005 (Tuesday)	2:00 – 4:00pm
Lectuee 1:	June 28, 2005 (Tuesday)	2:30 – 4:00pm

All lectures will be given in Room 517, Meng Wah Complex

All are Welcome