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Discrete equivalence of non-positive at infinity plane valuations

Carlos Galindo, Francisco Monserrat, Carlos-Jesús Moreno-Ávila

Abstract

Non-positive at infinity valuations are a class of real plane valuations which have a nice geometrical behavior. They are divided in three types. We study the dual graphs of non-positive at infinity valuations and give an algorithm for obtaining them. Moreover we compare these graphs attending the type of their corresponding valuation.

Discrete equivalence of non-positive at infinity plane valuations

Abstract

Non-positive at infinity valuations are a class of real plane valuations which have a nice geometrical behavior. They are divided in three types. We study the dual graphs of non-positive at infinity valuations and give an algorithm for obtaining them. Moreover we compare these graphs attending the type of their corresponding valuation.

Paper Structure

This paper contains 10 sections, 5 theorems, 33 equations, 1 figure.

Key Result

Theorem \oldthetheorem

Let $\nu_n$ be a divisorial plane valuation of $Z_0$. Set $Z$ the surface defined by $\nu_n$. Then

Figures (1)

  • Figure 1: Dual graph of a divisorial valuation

Theorems & Definitions (14)

  • Definition \oldthetheorem
  • Definition \oldthetheorem
  • Theorem \oldthetheorem
  • Definition \oldthetheorem
  • Proposition \oldthetheorem
  • Lemma \oldthetheorem
  • proof
  • Theorem \oldthetheorem
  • proof
  • Theorem \oldthetheorem
  • ...and 4 more