Decorated sheaves and morphisms in tilted hearts

Yinbang Lin; Sz-Sheng Wang; Bingyu Xia

doi:10.4134/JKMS.j230331

Journal of the
Korean Mathematical Society JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2024; 61(6): 1073-1093

Online first article October 17, 2024 Printed November 1, 2024

https://doi.org/10.4134/JKMS.j230331

Decorated sheaves and morphisms in tilted hearts

Yinbang Lin, Sz-Sheng Wang, Bingyu Xia

Tongji University; National Yang Ming Chiao Tung University; Shing-Tung Yau Center of Southeast University

Abstract

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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: Decorated sheaf, $t$-structure, moduli space, Quot space, tilt

MSC numbers: Primary 14D20, 14F08; Secondary 14D22, 14D23

Supported by: YL is supported by the Fundamental Research Funds for the Central Universities and Applied Basic Research Programs of Science and Technology Commission Foundation of Shanghai Municipality. SSW is supported by the Fundamental Research Funds for the Central Universities 2242020R10048 and the MOST under grant number 111-2115-M-001-003-MY3.