After a brief introduction to jet schemes, this article surveys their applications in singularity
theory (Nash problem, motivic integration, birational geometry, jet components graph …

The study of singularities of pairs is fundamental for higher dimensional birational geometry.
The usual approach to invariants of such singularities is via divisorial valuations, as in [Kol] …

The embedded Nash problem for a hypersurface in a smooth algebraic variety is to
characterize geometrically the maximal irreducible families of arcs with fixed order of contact …

Minimality of a toric embedded resolution of singularities after Bouvier-Gonzalez-Sprinberg
Page 1 MINIMALITY OF A TORIC EMBEDDED RESOLUTION OF SINGULARITIES AFTER …

Nash's problem concerning arcs poses the question of whether it is possible to construct a
bijective relationship between the minimal resolution of a surface singularity and the …

We solve the equivariant generalized Nash problem for any non-rational normal variety with
torus action of complexity one. Namely, we give an explicit combinatorial description of the …

Nash's problem concerning arcs poses the question of whether it is possible to construct a
bijective relationship between the minimal resolution of a surface singularity and the …

Jet Schemes of a singularity Page 1 JET SCHEMES OF A SINGULARITY BÜSRA KARADENIZ
SEN Let X ⊂ C3 be the hypersurface obtained as the zero locus of f(x, y, z) ∈ C[x, y, z]. Let m …

Let f∈ C [x, y, z]. The vanishing set of f defines an hypersurface X in C3. We are interested in
finding a toric resolution of X when X has singularity along one of the axes. We construct a …