Geometric model for vector bundles via infinite marked strips

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. By establishing a bijection between indecomposable bundles and orbits of line segments on the strip, we interpret dimensions of extension spaces as intersection indices of these line segment orbits. Furthermore, our investigation yields geometric interpretations for various aspects, including the slope of indecomposable bundles, the Picard group action, vector bundle duality, projective covers and injective hulls of extension bundles.