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The embedded Nash problem in singular spaces: the case of surfaces

Javier de la Bodega

Abstract

We introduce the embedded Nash problem allowing singularities in the ambient space, and solve it in the case of surfaces, generalizing \cite[Theorem 1.22]{BdlB}.

The embedded Nash problem in singular spaces: the case of surfaces

Abstract

We introduce the embedded Nash problem allowing singularities in the ambient space, and solve it in the case of surfaces, generalizing \cite[Theorem 1.22]{BdlB}.
Paper Structure (13 sections, 17 theorems, 65 equations)

This paper contains 13 sections, 17 theorems, 65 equations.

Table of Contents

  1. Introduction
  2. embedded Nash problem
  3. Arc spaces
  4. Contact loci
  5. Connection to maximal divisorial sets
  6. The subsets $\mathcal{X}_{m,E}$ are cylinders
  7. The problem
  8. A topological necessary condition for adjacencies to happen
  9. The case of surfaces
  10. Allowed adjacencies
  11. Forbidden adjacencies
  12. The A'Campo space
  13. Comparison with the smooth-ambient case

Key Result

Proposition 2.3

Let $E$ be an $m$-divisor. Then the generic point of $C_X(w_E)$ lies in $\mathcal{X}_{m,E}$. In particular, the closure of $\mathcal{X}_{m,E}$ in $\mathcal{L}(X)$ is $C_X(w_E)$.

Theorems & Definitions (45)

  • Definition 2.1
  • Definition 2.2: McL
  • Proposition 2.3
  • proof
  • Definition 2.4
  • Definition 2.5
  • Remark 2.6
  • Proposition 2.7: EM
  • Proposition 2.8
  • proof
  • ...and 35 more