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, parameterizing m-th jets on S. The fiber over the singular locus of S is called the singular fiber.
In this talk, 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.