Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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DECORATED SHEAVES AND MORPHISMS IN TILTED HEARTS

  • Yinbang Lin (School of Mathematical Sciences Tongji University) ;
  • Sz-Sheng Wang (Department of Applied Mathematics National Yang Ming Chiao Tung University) ;
  • Bingyu Xia (Shing-Tung Yau Center of Southeast University)
  • Received : 2023.06.22
  • Accepted : 2024.04.19
  • Published : 2024.11.01
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Abstract

We identify stable pairs and stable framed sheaves as epimorphisms and monomorphisms in the hearts of tilted t-structures under appropriate conditions. We then identify the moduli spaces with the corresponding Quot spaces. As a result, we obtain the projectivity of the Quot spaces in absolute cases. In addition, we prove a formula in a motivic Hall algebra, which relates together the Quot spaces under a tilt.

Keywords

Acknowledgement

We would like to thank Dingxin Zhang for helpful discussions and the referee for helpful suggestions. BYX thanks Morningside Center of Mathematics and Shing-Tung Yau Center of Southeast University for providing a stimulating environment. SSW thanks Shing-Tung Yau Center of Southeast University and Institute of Mathematics at Academia Sinica for providing a stimulating environment.

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