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.