Asian Journal of Mathematics

Volume 19 (2015)

Number 5

Wild quotient surface singularities whose dual graphs are not star-shaped

Pages: 951 – 986



Hiroyuki Ito (Department of Mathematics, Faculty of Science and Technology, Tokyo University of Science, Noda, Chiba, Japan)

Stefan Schröer (Mathematisches Institut, Heinrich-Heine-Universität, Düsseldorf, Germany)


We obtain 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.


wild quotient singularities, local fundamental groups, Hermitian curves

2010 Mathematics Subject Classification

14B05, 14H37

Published 20 November 2015