Project Details
Projekt
Moduli spaces of holomorphic vector bundles and Gauge theory on Calabi-Yau manifolds, with applications to F-theory/heterotic duality
Applicant
Professor Dr. Herbert Kurke
Subject Area
Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
Term
from 2000 to 2006
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 5253164
Study of the algebraic-geometric background of string-theory. The main achievement is to study moduli spaces relevant for F-theory/heterotic string duality. To understand the geometry of these moduli spaces of vector bundles on elliptically fibred Calabi-Yau manifolds we intend to develop further the so called graph method introduced by Braam and Hurtubise, in order to relate the moduli space of vector bundles on the section of the elliptic fibration (assuming the case of an elliptic fibration with a section) and the jumping behavior on the fibres. We also intend to give a direct algebraic geometric description of moduli-spaces of principal fibre bundles, at least for E8 or E8 x E8-bundles, and of a "universal family", starting with a linear-algebra construction of the corresponding Lie-algebra.
DFG Programme
Priority Programmes
