Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

On holomorphic tubular neighborhoods of compact Riemann surfaces

Satoshi Ogawa

Abstract

We give a sufficient condition for the existence of a holomorphic tubular neighborhood of a compact Riemann surface holomorphically embedded in a non-singular complex surface. Our sufficient condition is described by an arithmetical condition of unitary flat line bundles which can be regarded as an analogue of the Brjuno condition for irrational numbers which appears in the theory of 1-variable complex dynamics.

On holomorphic tubular neighborhoods of compact Riemann surfaces

Abstract

We give a sufficient condition for the existence of a holomorphic tubular neighborhood of a compact Riemann surface holomorphically embedded in a non-singular complex surface. Our sufficient condition is described by an arithmetical condition of unitary flat line bundles which can be regarded as an analogue of the Brjuno condition for irrational numbers which appears in the theory of 1-variable complex dynamics.
Paper Structure (15 sections, 62 equations)

This paper contains 15 sections, 62 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Čech coboundary equations with estimates
  4. Kodaira--Spencer type estimate
  5. Donin type estimate
  6. Gong--Stolovitch's result
  7. On the Brjuno condition
  8. The invariance of Brjuno condition
  9. Example
  10. On Hörmander type estimate
  11. Proof of Theorem \ref{['main']}
  12. Čech--Dolbeault correspondence
  13. An estimate of $K(T_C\otimes E)$ by using perturbed $\overline{\partial}$-operators
  14. Proof of Theorem \ref{['main']}
  15. Ueda's lemma and Donin type estimate for the $L^\infty$-norm

Theorems & Definitions (13)

  • proof
  • proof
  • proof
  • proof
  • proof
  • proof : Proof of proposition \ref{['correspondenceKS']}.
  • proof
  • proof
  • proof
  • proof
  • ...and 3 more