The small-characteristic bound for Poisson traces of quasihomogeneous surface singularities

Let $A$ be the algebra of regular functions on a quasihomogeneous isolated surface singularity $X$ defined by $Q(x,y,z)=0$ over a field of characteristic $p$, with the notation $a,b,c,d$ and $h_{A/\lbrace A,A\rbrace}(t)$ as in Theorem 1. Small-characteristic bound. The formula of Theorem 1 for $h_{A/\lbrace A,A\rbrace}(t)$ holds whenever $p>2d-a-b-c$. In particular, for Kleinian singularities it holds for $p>h$, and for cones over smooth projective curves of degree $d$ it holds for $p>2d-3$. These bounds concern when the large-characteristic formula is expected to remain valid in the examples under consideration; the claim is presented as conjectural and is based on computer evidence and intuition.