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

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