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Co-Higgs bundles of Schwarzenberger type and the determinant morphism

Kuntal Banerjee

Abstract

We identify images of the determinant morphism of trace-free co-Higgs bundles modeled on rank 2 Schwarzenberger bundles.

Co-Higgs bundles of Schwarzenberger type and the determinant morphism

Abstract

We identify images of the determinant morphism of trace-free co-Higgs bundles modeled on rank 2 Schwarzenberger bundles.

Paper Structure

This paper contains 6 sections, 7 theorems, 38 equations.

Table of Contents

  1. Introduction
  2. Overview
  3. Acknowledgments
  4. The determinant morphism on co-Higgs bundles of Schwarzenberger type
  5. Preliminaries
  6. Schwarzenberger bundles and determinant morphism

Key Result

Theorem 2.1.2

(gallego2023higgs, Simp2) Hitchin morphism $\mathcal{H}: \mathcal{M}_{X, H^k}^{ss}(P, V)\to \mathcal{B}(r)=\oplus_{i=1}^r H^0(X, \emph{Sym}^iV)$ is proper.

Theorems & Definitions (19)

  • Definition 2.1.1
  • Theorem 2.1.2
  • Definition 2.2.1
  • Lemma 2.2.2
  • proof
  • Lemma 2.2.3
  • proof
  • Theorem 2.2.4
  • proof
  • Remark 2.2.5
  • ...and 9 more