Geometric model for vector bundles via infinite marked strips

TL;DR

This paper introduces a geometric model for vector bundles over weighted projective lines of type (2,2,n), using infinite marked strips and group actions to interpret bundle properties.

Contribution

It provides a novel geometric framework linking vector bundles to orbits of line segments on an infinite marked strip, offering new insights into their structure and symmetries.

Findings

Established a bijection between indecomposable bundles and orbits of line segments.

Provided geometric interpretations for Picard group action and duality.

Analyzed dimensions of extension groups and properties of projective/injective covers.

Abstract

We present a geometric model for the category of vector bundles over the weighted projective line of type (2,2,n). This model is based on the orbit space of an infinite marked strip under a specific group action. We establish a bijection between indecomposable bundles and orbits of line segments on the strip, which yields geometric interpretations for various aspects, including the Picard group action, vector bundle duality, dimension of extension group, projective cover and injective hull of extension bundle, etc.