Abstract
We give a explicit description of gluing stability conditions on ruled surfaces by introducing gluing perversity. Moreover, we describe a destabilizing wall of skyscraper sheaves on ruled surfaces by deformation of stability conditions glued from $\widetilde{GL^{+}}(2,\mathbb{R})$-translates of the standard stability condition on the base curve.
Acknowledgments
The author would like to thank his surpervisor Prof. Yasunari Nagai for providing a great deal of help and continuously warm encouragement. He would also like to thank Prof. Yukinobu Toda, Prof. Hajime Kaji, Prof. Ryo Ohkawa, Prof. Daizo Ishikawa and Prof. Seung-Jo Jung for many valuable comments, discussion and pointing out his mistakes. Finally would like to thank the referee of Osaka Journal of Mathematics for many kind suggestions and pointing out his mistakes.
Citation
Takayuki Uchiba. "On gluing stability conditions on ruled surfaces of positive genus." Osaka J. Math. 58 (3) 647 - 660, July 2021.
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