English

Arc spaces of cA-type singularities

Algebraic Geometry 2013-06-06 v1

Abstract

We study the space of arcs on a singularity of the form xy=f(z_1,..., z_n) and prove 2 main results. (i) The number of irreducible components equals the multiplicity of f minus 1. (ii) If n>1 and the leading homogeneous term of f is not a perfect square then the Nash map from the set of irreducible components to the set of essential divisors is not surjective.

Keywords

Cite

@article{arxiv.1306.1208,
  title  = {Arc spaces of cA-type singularities},
  author = {Jennifer M. Johnson and János Kollár},
  journal= {arXiv preprint arXiv:1306.1208},
  year   = {2013}
}

Comments

This paper supersedes arXiv:1207.5036

R2 v1 2026-06-22T00:28:43.592Z