Let be a rational double point defined over an algebraically closed field of characteristic . We evaluate further the dimensions of the local cohomology groups, which were treated by Wahl in 1975 as vanishing theorem C (resp., D) under the assumption that is a very good prime (resp., good prime) with respect to . We use Artin’s classification of rational double points and completely determine the dimensions and , supplementing Wahl’s theorems. In the proof, we concretely construct derivations that do not lift to the minimal resolution and an equisingular family that injects into a versal deformation of the rational double point .
"Further Evaluation of Wahl Vanishing Theorems for Surface Singularities in Characteristic ." Michigan Math. J. 68 (3) 621 - 636, August 2019. https://doi.org/10.1307/mmj/1560391418