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Tilting bundles for weighted projective lines of weight type $(p,q)$

Volume 163 / 2021

Xiaofeng Zhang Colloquium Mathematicum 163 (2021), 197-210 MSC: Primary 14F05, 14H45; Secondary 16G70, 18E30. DOI: 10.4064/cm7905-9-2019 Published online: 19 June 2020

Abstract

We give a combinatorial description of tilting bundles in the category of coherent sheaves over the weighted projective line of type $(p,q)$. We define a set of admissible paths in the rectangular area $\mathbb {D}_{(p,q)}=[1,p-1]\times [1,q-1]$, and show that there is a bijection between the fundamental tilting bundles and the admissible paths in $\mathbb {D}_{(p,q)}$.

Authors

  • Xiaofeng ZhangSchool of Computer and Artificial Intelligence
    Xiamen Institute of Technology
    Xiamen 361021, China
    e-mail

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