Arcs on rational double points in arbitrary characteristic
Tommaso de Fernex and Shih-Hsin WangWith an appendix by Tommaso de Fernex, Roi Docampo, and Gebhard Martin
Supplement to: Arcs on rational double points in arbitrary characteristic
Journal of Singularities
volume 29 (2026), 254-270
Received: 10 September 2025. In revised form: 24 July 2026
Abstract:
We settle the Nash problem for two-dimensional rational double points in all characteristics. The proof is based on a direct computation of the families of arcs through these singularities.
2020 Mathematical Subject Classification:
Primary 14E18; Secondary 14J17
Key words and phrases:
Nash problem, jet scheme, rational double points
Author(s) information:
Tommaso de Fernex
Department of Mathematics
University of Utah
Salt Lake City, UT 84112, USA
email: defernex@math.utah.edu
Shih-Hsin Wang
Department of Mathematics
University of Utah
Salt Lake City, UT 84112, USA
email: shwang@math.utah.edu