Bounds on generators and relations for the algebra of $SL_2(\C)$ conformal blocks

TL;DR

This paper investigates the algebraic structure of the Cox ring associated with the moduli space of $SL_2( ext{C})$ quasi-parabolic bundles, demonstrating generation by low-level conformal blocks and describing the ideal's generators.

Contribution

It establishes that the Cox ring is generated by conformal blocks of levels 1 and 2 and identifies the degrees of generators of the defining ideal.

Findings

Cox ring generated by conformal blocks of levels 1 and 2

Ideal generated by forms of degrees 2, 3, 4

Provides bounds on generators and relations for the algebra

Abstract

We show that the Cox ring of the moduli of $SL_2(\C)$ quasi-parabolic principal bundles on a marked curve is generated by conformal blocks of level 1 and 2. We show that the ideal which vanishes on these generators is generated by forms of degrees $2, 3, 4.$