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Bounded t-Structures on the Bounded Derived Category of Coherent Sheaves over a Weighted Projective Line

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Abstract

We use recollement and HRS-tilt to describe bounded t-structures on the bounded derived category \(\mathcal {D}^{b}(\mathbb {X})\) of coherent sheaves over a weighted projective line \(\mathbb {X}\) of domestic or tubular type. We will see from our description that the combinatorics in the classification of bounded t-structures on \(\mathcal {D}^{b}(\mathbb {X})\) can be reduced to that in the classification of bounded t-structures on the bounded derived categories of finite dimensional right modules over representation-finite finite dimensional hereditary algebras.

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Acknowledgements

The question of this article originated from a seminar on Bridgeland’s stability conditions organized by Prof. Xiao-Wu Chen, Prof. Mao Sheng and Prof. Bin Xu. I thank these organizers who gave me the opportunity to report. I am grateful to the participants for their patience and critical questions. Thanks are once again due to Prof. Xiao-Wu Chen, my supervisor, for his guidance and kindness.

I thank Peng-Jie Jiao for discussion, thank Prof. Helmut Lenzing for carefully answering my question on stable bundles over a tubular weighted projective line, thank Prof. Zeng-Qiang Lin for communication on realization functors, thank Prof. Hagen Meltzer for his lectures on weighted projective lines, thank Prof. Dong Yang for explaning the results in [28] and for stimulating conversations, and thank Prof. Pu Zhang for a series of lectures on triangulated categories based on his newly-written book titled “triangulated categories and derived categories” (in Chinese).

Moreover, I would like to express my deep gratitude to two anonymous referees. The referee of the first version of this article gave me a long list of suggestions, which pointed out many mistakes and inaccuracies and helped in improving the exposition and in reshaping some parts of this article. Another referee of the second version of this article also poinited out several mistakes, many typos and grammar problems.

This work is supported by the National Science Foundation of China (No. 11522113 and No. 115771329) and also by the Fundamental Research Funds for the Central Unviersities.

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  1. School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui, 230026, People’s Republic of China

    Chao Sun

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Sun, C. Bounded t-Structures on the Bounded Derived Category of Coherent Sheaves over a Weighted Projective Line. Algebr Represent Theor 23, 2167–2235 (2020). https://doi.org/10.1007/s10468-019-09929-w

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