Tilting Objects via Recollements and $p$-Cycles on Weighted Projective Lines

Qiang Dong; Hongxia Zhang

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arXiv · 2510.03208

Tilting Objects via Recollements and $p$-Cycles on Weighted Projective Lines

Qiang Dong·Hongxia Zhang

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Abstract

In this paper, we provide a new method for constructing tilting objects in a triangulated category via recollements. The $p$-cycle approach to exceptional curve processes significant advantages in constructing recollements and ladders, due to the existence of reduction/insertion functors. In order to construct tilting objects in the stable category of vector bundles over a weighted projective line, we give explicit expressions for line bundles and extension bundles due to the $p$-cycles constuctions. Furthermore, we provide an essential proof for tilting cuboic object and tilting objects consisting of Auslander bundles. Moreover, we construct certain new tilting objects in the stable category of vector bundles over a weighted projective line.

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BibTeX RIS

Qiang Dong, Hongxia Zhang. 2025-10-03. Tilting Objects via Recollements and $p$-Cycles on Weighted Projective Lines. https://arxiv.org/abs/2510.03208

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