CM minimization and special K-stability
- December 16 (Fri) at 14:00 - 16:30, 2022 (JST)
- Mr. Masafumi Hattori (Ph.D. Students, Department of Mathematics, Graduate School of Science, Kyoto University)
- via Zoom
- Eiji Inoue
Odaka proposed a conjecture predicting that the degrees of CM line bundles for families with fixed general fibers are strictly minimized if the special fibers are K-stable. This conjecture is called CM minimization and a quantitative strengthening of the conjecture of separatedness of moduli spaces of K-stable varieties (K-moduli). This conjecture was already shown for K-ample (Wang-Xu), Calabi-Yau (Odaka) and Fano varieties (Blum-Xu). In this talk, we introduce a new class, special K-stable varieties, and settle CM minimization for them, which is a generalization of the above results. In addition, we would like to explain an important application of this, construction of moduli spaces of uniformly adiabatically K-stable klt trivial fibrations over curves as a separated Deligne-Mumford stack in a joint work with Kenta Hashizume to appear. This is based on arXiv:2211.03108.
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