Abstract
We introduce $\mathfrak{f}$-stability, a modification of fibration stability of Dervan-Sektnan [11], and show that $\mathfrak{f}$-semistable fibrations have only semi log canonical singularities. Moreover, $\mathfrak{f}$-stability puts restrictions on semi log canonical centers on Fano fibrations.
Acknowledgments
The author cannot express enough his sincere and deep gratitude to Professor Yuji Odaka who is his research advisor for a lot of suggestive advices, productive discussions and reading the draft. The author also would like to thank Professor Ruadhaí Dervan and the anonymous referee for helpful comments, which improve this paper. This work is a part of his master thesis and partially supported by JSPS KAKENHI 22J20059 (Grant-in-Aid for JSPS Fellows DC1).
Citation
Masafumi Hattori. "On fibration stability after Dervan-Sektnan and singularities." Osaka J. Math. 61 (2) 195 - 228, April 2024.
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