Spectral coverings without embeddings

TL;DR

This paper explores a relaxed spectral correspondence for twisted Higgs bundles, constructing them from finite coverings and vector bundles without matching eigen-data, and analyzes their stability compared to traditional spectral covers.

Contribution

It introduces a novel approach to constructing twisted Higgs bundles from coverings, bypassing the need for eigen-data matching, and studies their stability properties.

Findings

Constructed twisted Higgs bundles from finite coverings and vector bundles.

Compared stability of these bundles to traditional spectral covers.

Provided insights into the spectral correspondence without embeddings.

Abstract

In this article, we investigate a weakened version of the spectral correspondence for twisted Higgs bundles. Namely, we construct twisted Higgs bundles from a finite covering map and a vector bundle on that covering but without requiring that they match the eigen-data for some fixed twisted Higgs bundle. We investigate stability for twisted Higgs bundles constructed in this way, and compare our covering data to that of the traditional spectral cover.