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Curves of best approximation on wonderful varieties

Christopher Manon, David McKinnon, Matthew Satriano

Abstract

We give an unconditional proof of the Coba conjecture for wonderful compactifications of adjoint type for semisimple Lie groups of type $A_n$. We also give a proof of a slightly weaker conjecture for wonderful compactifications of adjoint type for arbitrary Lie groups.

Curves of best approximation on wonderful varieties

Abstract

We give an unconditional proof of the Coba conjecture for wonderful compactifications of adjoint type for semisimple Lie groups of type . We also give a proof of a slightly weaker conjecture for wonderful compactifications of adjoint type for arbitrary Lie groups.

Paper Structure

This paper contains 6 sections, 2 theorems, 11 equations, 2 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. The Coba Conjecture
  4. Geometry of the wonderful compactification
  5. Main Theorem for wonderful compactifications of adjoint type
  6. Tables

Key Result

Proposition 2.6

Let $D$ be a divisor on an $n$-dimensional variety $X$ over a number field $K$. If then for every smooth point $P\in X(K)$ and every Zariski dense sequence $\{x_i\}$ of rational points, we have

Theorems & Definitions (9)

  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • Conjecture 2.4: Coba conjecture
  • Conjecture 2.5: near-Coba conjecture
  • Proposition 2.6
  • proof
  • Remark 2.7
  • Theorem 3.1