WILD QUOTIENT SURFACE SINGULARITIES WHOSE DUAL GRAPHS ARE NOT STAR-SHAPED

We obtain some results that answer certain questions of Lorenzini on wild quotient singularities in dimension two. Using Kato’s theory of log structures and log regularity, we prove that the dual graph of exceptional curves on the resolution of singularities contains at least one node. Furthermore, we show that diagonal quotients for Hermitian curves by analogues of Heisenberg groups lead to examples of wild quotient singularities where the dual graph contains at least two nodes.
Contents Introduction 1. Generalities on wild quotient singularities 2. Dual graphs without nodes 3. Local fundamental groups 4. Cotangent spaces 5. Hermitian curves and special p-groups 6. Quotient singularities with two nodes 7. Description of the generic fiber 8. Computation of the singular fiber 9. Higher ramification groups