Generic non-splice-quotient conjecture for surface singularities

Fix a rational homology sphere link and consider the general' $\mathbb{Q}$-Gorenstein singularity with that link. Suppose that its fundamental cycle has arithmetic genus at least $3$. **Generic non-splice-quotient conjecture.** The singularity is not a splice quotient, and its universal abelian cover is not a complete intersection. The claim is motivated by the authors' computations and is stated as a conjecture about the general behavior; the meaning of general' is noted as unclear when a suitable moduli space is not known. It excludes rational and elliptic singularities and the case in which the exceptional curve is hyperelliptic.