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On a theorem of Schmidt's subspace theory with moving targets

GuanHeng Zhao, YuXi Li

Abstract

The Schmidt's subspace theory with moving targets, as a significant branch in this field, has been substantially developed in recent years. We continue the approach of the previous work, construct a weighted version of generalized Schmidt subspace theory with moving targets. As a supplement and sharp extension to the relevant results.

On a theorem of Schmidt's subspace theory with moving targets

Abstract

The Schmidt's subspace theory with moving targets, as a significant branch in this field, has been substantially developed in recent years. We continue the approach of the previous work, construct a weighted version of generalized Schmidt subspace theory with moving targets. As a supplement and sharp extension to the relevant results.
Paper Structure (12 sections, 11 theorems, 78 equations)

This paper contains 12 sections, 11 theorems, 78 equations.

Table of Contents

  1. Preliminary knowledge
  2. Cardinal conditions
  3. Height
  4. Weil function (local height function)
  5. Moving hypersurfaces/polynomials
  6. Family of moving targets
  7. Subgeneral position
  8. Seshadri constants
  9. Introduction
  10. An auxiliary result in algebra
  11. The Inertia Form Method
  12. Proof of the Main Theorem

Key Result

Lemma 1.5

Let $A \subset \Lambda$ be coherent with respect to $\mathcal{Q}$, supposed they are in general position. Then for each $J \subset\{1, \ldots, q\}$ with $\sharp J=n+1$, there are functions $\gamma_{1, v}, \gamma_{2, v} \in \mathcal{C}_{\mathbf{x}}$ such that for all $\alpha \in A$ ouside finite subset and all $v \in S$.

Theorems & Definitions (23)

  • Definition 1.1: coherent
  • Definition 1.2: Special representatives
  • Definition 1.3: $V$-algebraically non-degenerate
  • Remark 1.4
  • Lemma 1.5
  • Definition 1.6
  • Definition 1.7
  • Remark 1.8
  • Theorem 2.1
  • Theorem 2.2
  • ...and 13 more