Jet schemes of singular surfaces of types D_4^0 and D_4^1 in characteristic 2
Yoshimune Koreeda
Journal of Singularities
volume 27 (2024), 167-192
Received: 30 April 2024. In revised form: 28 October 2024
Abstract:
Let k be an algebraically closed field, S a variety over k and m a nonnegative integer. There is a space S_m over S, called the jet scheme of S of order m, parametrizing m-th jets on S. The fiber over the singular locus of S is called the singular fiber.
In this paper, we consider the singular fibers of the jet schemes of 2-dimensional rational double points over a field k of characteristic 2 whose resolution graph is of type D_4. There are two types of such singularities, of type D_4^0 and type D_4^1. We give the irreducible decomposition of the singular fiber and describe the configuration of the irreducible components. The case of a D_4^0-singularity is quite similar to the case of characteristic 0 studied in the previous paper. The case of D_4^1-singularity requires more elaborate analysis of certain subsets of the singular fibers.
2010 Mathematical Subject Classification:
Primary 14J17
Key words and phrases:
Jet scheme; rational double point singularities; positive characteristic
Author(s) information:
Yoshimune Koreeda
Department of Mathematics
Graduate School of Science
Hiroshima University
1-3-1 Kagamiyama
Higashi-Hiroshima, 739-8526 ,
Japan
email: y-koreeda@hiroshima-u.ac.jp