Geometric model for vector bundles via infinite marked strips

Jianmin Chen; Jinfeng Zhang; Shiquan Ruan

Geometric model for vector bundles via infinite marked strips

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arxiv 2405.07793 v2 pith:FETOWLS5 submitted 2024-05-13 math.RT

Jianmin Chen , Shiquan Ruan , Jinfeng Zhang This is my paper · ORCID

classification math.RT

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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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Geometric-combinatorial approaches to tilting theory for weighted projective lines
math.RT 2025-01 conditional novelty 6.0 of 10

Indecomposable sheaves on the weighted projective line (2,2,n) are bijectively drawn as skew-curves on a symmetric cylinder, with pseudo-triangulations corresponding exactly to tilting sheaves and flips to mutations.

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