On the embedded Nash problem
Algebraic Geometry
2024-11-20 v2
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.
Cite
@article{arxiv.2208.08546,
title = {On the embedded Nash problem},
author = {Nero Budur and Javier de la Bodega and Eduardo de Lorenzo Poza and Javier Fernández de Bobadilla and Tomasz Pełka},
journal= {arXiv preprint arXiv:2208.08546},
year = {2024}
}
Comments
v2: The main change is in the proof of Thm 7.4. To appear in Forum Math. Pi