Differential geometry of holomorphic vector bundles on a curve
Florent Schaffhauser
TL;DR
This paper introduces differential-geometric techniques for studying holomorphic vector bundles on compact Riemann surfaces, providing foundational insights relevant to geometric and topological methods in quantum field theory.
Contribution
It offers an accessible introduction to the differential geometry of holomorphic vector bundles on curves, connecting complex geometry with quantum field theory applications.
Findings
Provides a comprehensive overview of differential-geometric methods
Connects complex geometry with quantum field theory concepts
Serves as an educational resource for advanced geometry studies
Abstract
These notes are based on a series of five lectures given at the 2009 Villa de Leyva Summer School on Geometric and Topological Methods for Quantum Field Theory. The purpose of the lectures was to give an introduction to differential-geometric methods in the study of holomorphic vector bundles on a compact connected Riemann surface.
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Taxonomy
TopicsGeometry and complex manifolds · Algebraic Geometry and Number Theory · Advanced Differential Equations and Dynamical Systems