On the embedded Nash problem

Abstract

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 along the hypersurface. We show that divisors on minimal models of the pair contribute with such families. We solve the problem for unibranch plane curve germs, in terms of the resolution graph. These are embedded analogs of known results for the classical Nash problem on singular varieties.

v2: The main change is in the proof of Thm 7.4. To appear in Forum Math. Pi

References in corpus (8)

• Motivic Igusa zeta functions
• Jet Schemes of Locally Complete Intersection Canonical Singularities
• Motivic Serre invariants, ramification, and the analytic Milnor fiber
• Arcs on Determinantal Varieties
• Terminal valuations and the Nash problem
• Floer Cohomology, Multiplicity and the Log Canonical Threshold
• On the generalized Nash problem for smooth germs and adjacencies of curve singularities
• Jet schemes of quasi-ordinary surface singularities