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Zariski invariant for quasi-ordinary hypersurfaces

Rafael Afonso Barbosa, Marcelo Escudeiro Hernandes

Abstract

We introduced an $\tilde{\mathcal{A}}$-invariant for quasi-ordinary parameterizations and we consider it to describe quasi-ordinary surfaces with one generalized characteristic exponent admitting a countable moduli.

Zariski invariant for quasi-ordinary hypersurfaces

Abstract

We introduced an -invariant for quasi-ordinary parameterizations and we consider it to describe quasi-ordinary surfaces with one generalized characteristic exponent admitting a countable moduli.
Paper Structure (5 sections, 12 theorems, 86 equations)

This paper contains 5 sections, 12 theorems, 86 equations.

Table of Contents

  1. Introduction
  2. Quasi-ordinary parameterizations
  3. Generalized Zariski exponents
  4. Quasi-simple surface singularities
  5. Technical Lemmas

Key Result

Proposition 2.5

Let $H = \left(t^n_1,\ldots, t^n_r, S(\underline{t})\right)$ be a q.o. parameterization. If $P\subseteq \{\zeta-\lambda_{1};\ \lambda_{1}\neq\zeta\in supp(S(\underline{t}))\}\subset\mathbb{R}^{r}$ is a linearly independent set, then there exists $(\sigma, \rho) \in \mathcal{H}$ such that all terms w

Theorems & Definitions (33)

  • Definition 2.1
  • Remark 2.2
  • Definition 2.3
  • Definition 2.4
  • Proposition 2.5: Proposition 2.5 in Marcelo-Nayene
  • Proposition 2.6: Corollary 3.6 in Marcelo-Nayene
  • Proposition 3.1
  • proof
  • Example 3.2
  • Example 3.3
  • ...and 23 more