An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces

• Main Author: Schlichenmaier, Martin (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2007.
• Edition: Second Edition.
• Series: Theoretical and Mathematical Physics,
• Subjects: Physics.; Algebraic topology.; Elementary particles (Physics).; Quantum field theory.; Theoretical, Mathematical and Computational Physics.; Elementary Particles, Quantum Field Theory.; Algebraic Topology.

Table of Contents:

• Manifolds
• Topology of Riemann Surfaces
• Analytic Structure
• Diffierentials and Integration
• Tori and Jacobians
• Projective Varieties
• Moduli Spaces of Curves
• Vector Bundles, Sheaves and Cohomology
• The Theorem of Riemann–Roch for Line Bundles
• The Mumford Isomorphism on the Moduli Space
• TopoModern Algebraic Geometry
• Schemes
• Hodge Decomposition and K¨ahler Manifold
• Calabi-Yau Manifolds and Mirror Symmetry.