Stability properties of adapted tangent sheaves on K\"ahler--Einstein log Fano pairs

Abstract

Let $(X, \Delta)$ be a log Fano pair with standard coefficients endowed with a singular K\"ahler--Einstein metric. We show that the adapted tangent sheaf $\mathcal{T}_{X, \Delta, f}$ and the adapted canonical extension $\mathcal{E}_{X, \Delta, f}$ are polystable with respect to $f^*c_1(X, \Delta)$ for any strictly $\Delta$-adapted morphism $f: Y \to X$.