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On The Image Of The Hilbert Map

Jingzhou Sun

Abstract

We talk about the image of the Hilbert map. We show the necessary and sufficient condition that the Hilbert map is surjective.

On The Image Of The Hilbert Map

Abstract

We talk about the image of the Hilbert map. We show the necessary and sufficient condition that the Hilbert map is surjective.
Paper Structure (3 sections, 5 theorems, 24 equations)

This paper contains 3 sections, 5 theorems, 24 equations.

Table of Contents

  1. Introduction
  2. proof of the main results
  3. discussion of constraints

Key Result

Theorem 1.1

Let $V\subset H^0(X,L)$ be a subspace that generates $L$, which is minimal in the sense that no proper subspace of $V$ generates $L$. Then ${\operatorname{Hilb}}_V$ is surjective.

Theorems & Definitions (9)

  • Theorem 1.1
  • Theorem 1.2
  • Theorem 1.3
  • Theorem 2.1: Aubin-Yau
  • Theorem 2.2
  • proof
  • proof
  • proof : proof of theorem \ref{['theo-points']}
  • proof : proof of theorem \ref{['thm-main']}