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arXiv · 2405.07793

Geometric model for vector bundles via infinite marked strips

Jianmin Chen·Shiquan Ruan·Jinfeng Zhang
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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.

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Jianmin Chen, Shiquan Ruan, Jinfeng Zhang. 2024-06-11. Geometric model for vector bundles via infinite marked strips. https://arxiv.org/abs/2405.07793

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