## Logarithmic projective flat connection for generalized [theta] functions

Grant Data

**Project Title**

Logarithmic projective flat connection for generalized [theta] functions

**Principal Investigator**

Dr Sun, Xiaotao
(Principal investigator)

**Duration**

24

**Start Date**

2002-09-01

**Completion Date**

2004-08-31

**Amount**

350000

**Conference Title**

**Presentation Title**

**Keywords**

mathematics

**Discipline**

Applied Mathematics

**Sponsor**

RGC General Research Fund (GRF)

**HKU Project Code**

HKU 7131/02P

**Grant Type**

General Research Fund (GRF)

**Funding Year**

2002/2003

**Status**

Completed

**Objectives**

To define a reasonable conformal field theory in algebraic geometry. Two basic problems have to be solved. One is to prove that when the curve moves in its moduli space, the associated vector spaces form a vector bundle and there is a logarithmic projective flat connection on this vector bundle. Another problem is to prove that any generalized theta function associated to a singular curve can be obtained from generalized [theta] functions associated to a smooth curve, normalization of the singular curve.