Book contents
- Frontmatter
- Dedication
- Contents
- Organization
- Acknowledgements
- 1 Introduction
- Part I Modular forms and their variants
- Part II Extensions and applications
- Part III Appendix
- Appendix A Some arithmetic
- Appendix B Riemann surfaces
- Appendix C Line bundles on Riemann surfaces
- Appendix D Riemann #-functions and meromorphic forms
- Appendix E Solutions to exercises
- References
- Index
Appendix C - Line bundles on Riemann surfaces
from Part III - Appendix
Published online by Cambridge University Press: 28 November 2024
Book contents
- Frontmatter
- Dedication
- Contents
- Organization
- Acknowledgements
- 1 Introduction
- Part I Modular forms and their variants
- Part II Extensions and applications
- Part III Appendix
- Appendix A Some arithmetic
- Appendix B Riemann surfaces
- Appendix C Line bundles on Riemann surfaces
- Appendix D Riemann #-functions and meromorphic forms
- Appendix E Solutions to exercises
- References
- Index
Summary
In this appendix, we shall define and study complex line bundles over an arbitrary compact Riemann surface, provide their topological classification in terms divisors, and give the Riemann–Roch theorem. We shall prove various dimension formulas, including for the dimension of the moduli space of complex or conformal structures on a Riemann surface. We then discuss sections of line bundles from a more physics-oriented point of view in terms of spaces of vector fields, differential forms, and spinor fields.
- Type
- Chapter
- Information
- Modular Forms and String Theory , pp. 378 - 390Publisher: Cambridge University PressPrint publication year: 2024