Conformal Blocks: Vector bundle structures, Sewing, and Factorization

Abstract

This is an informal note on the complex-analytic approach to the theory of conformal blocks for rational VOAs. Its main body was completed in November 2020.

LaTeX index issue corrected. Main body completed in Nov 2020 and intended as an informal note. A large part of its content was later adapted in works of the author and his collaborator, notably arXiv:2011.07450, 2110.04774, 2305.10180, 2411.07707. Please refer to these official works for formal treatments and references. This work was not polished and references incomplete. Use at your own risk