Resonance of rank-two vector bundles over elliptic curves

TL;DR

This paper investigates the resonance varieties of rank-two vector bundles over elliptic curves, focusing on flattening stratification and their relation to Grassmannian sections.

Contribution

It introduces a novel analysis of resonance varieties via flattening stratification and explores their connection with Grassmannian linear sections.

Findings

Resonance varieties are characterized through flattening stratification.

A new link between resonance and Grassmannian sections is established.

The approach provides insights into the geometric structure of vector bundles over elliptic curves.

Abstract

In this note, we study the resonance variety of rank-two vector bundles over an elliptic curve. Our approach is based on analyzing the flattening stratification of the resonance. We also investigate the linear section of the Grassmann variety $\operatorname{Gr}(2,n)$ from which the resonance is constructed through the lens of its corresponding flattening stratification.