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The Simplicity of the Hodge Bundle

Anand Patel

Abstract

This paper shows that the Hodge bundle over the moduli space of genus $g \geq 2$ curves does not contain any non-trivial sub-bundles. Notably, the mathematical content was generated by Aletheia, a custom AI agent powered by Gemini Deep Think.

The Simplicity of the Hodge Bundle

Abstract

This paper shows that the Hodge bundle over the moduli space of genus curves does not contain any non-trivial sub-bundles. Notably, the mathematical content was generated by Aletheia, a custom AI agent powered by Gemini Deep Think.
Paper Structure (8 sections, 6 theorems, 16 equations)

This paper contains 8 sections, 6 theorems, 16 equations.

Table of Contents

  1. Introduction
  2. Acknowledgments and use of AI
  3. Context and further directions
  4. Conventions
  5. The proof
  6. Curves with involutions
  7. Some curves with two commuting involutions
  8. Proof

Key Result

Theorem 1.1

The Hodge bundle $\Omega_{g}$ does not contain any non-trivial sub-bundles.

Theorems & Definitions (13)

  • Theorem 1.1
  • Lemma 2.1
  • proof
  • Definition 2.3
  • Lemma 2.4
  • proof
  • Lemma 2.5
  • proof
  • Lemma 2.7
  • proof
  • ...and 3 more