Chern classes of conformal blocks

TL;DR

This paper derives formulas for the Chern classes of conformal blocks bundles on moduli spaces of curves, providing tools for explicit calculations and exploring implications for specific Lie algebras and levels.

Contribution

It introduces a general formula for Chern classes of conformal blocks bundles and a method for computing their first Chern class on higher genus moduli spaces.

Findings

Derived a formula for Chern classes on _{0,n}

Explored consequences for sl_2 and level 1

Provided a method for higher genus computations

Abstract

We derive a formula for the Chern classes of the bundles of conformal blocks on \bar{M}_{0,n} associated to simple finite dimensional Lie algebras and explore its consequences in more detail for sl_2 and in general for level 1. We also give a method for computing the first Chern class of such bundles on \bar{M}_{g,n} for g>0.