Moduli spaces of holomorphic vector bundles and Gauge theory on Calabi-Yau manifolds, with applications to F-theory/heterotic duality

• Antragsteller: Professor Dr. Herbert Kurke
• Fachliche Zuordnung: Kern- und Elementarteilchenphysik, Quantenmechanik, Relativitätstheorie, Felder
• Förderung: Förderung von 2000 bis 2006
• Projektkennung: Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 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-Verfahren: Schwerpunktprogramme
• Teilprojekt zu: SPP 1096: Stringtheorie im Kontext von Teilchenphysik, Quantenfeldtheorie, Quantengravitation, Kosmologie und Mathematik