The Gorenstein property for projective coordinate rings of the moduli of parabolic $\mathrm{SL}_2$-principal bundles on a smooth curve

TL;DR

This paper investigates the Gorenstein property of projective coordinate rings associated with moduli spaces of parabolic SL_2-principal bundles on smooth curves, showing they are not Gorenstein under certain conditions.

Contribution

It provides a combinatorial approach to determine the Gorenstein property of these coordinate rings, revealing non-Gorenstein cases for higher genus and marked points.

Findings

Coordinate rings are not Gorenstein for genus > 1 and marked points > 1

Utilizes combinatorial methods for algebraic property analysis

Extends understanding of moduli space algebraic structures

Abstract

Using combinatorial methods, we determine that a projective coordinate ring of the moduli of parabolic principal $\mathrm{SL}_2$-bundles on a marked projective curve is not Gorenstein when the genus and number of marked points are greater than $1$.