CM minimization and special K-stability

Time:Thur., 15:30-16:30, Dec.8, 2022

Venue: Venue / 地点 Zoom ID: 455 260 1552, PW: YMSC

Organizer:Caucher Birkar,曲三太, 陈炳仪

Speaker:Masafumi Hattori (Kyoto University)


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.


Masafumi Hattori is a PhD student at Kyoto University. His rearsch field is Algebraic Geometry.

DATEDecember 8, 2022
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