The Gorenstein property for projective coordinate rings of the moduli of   parabolic $\mathrm{SL}_2$-principal bundles on a smooth curve
  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 $1$. 
Theodore Faust, Christopher Manon
math.AG