Room 515, Cosmology Building, National Taiwan University + Zoom, Physical+Online Seminar
(實體+線上演講 台灣大學次震宇宙館515研討室+ Zoom)
K-moduli of Fano Threefolds of Picard Rank 4 and Degree 24
Ivan Cheltsov (The University of Edinburgh)
Abstract
Smooth Fano threefolds of Picard rank 4 and degree 24 are divisors in
![](https://chart.googleapis.com/chart?cht=tx&chl=%24(%5Cmathbb%7BP%7D%5E1)%5E4%24&chf=bg,s,333333&chco=ffffff)
of degree
![](https://chart.googleapis.com/chart?cht=tx&chl=%24(1%2C1%2C1%2C1)%24&chf=bg,s,333333&chco=ffffff)
. All of them are K-stable by a theorem of Grisha Belousov and Costya Loginov from Moscow. It is natural to expect that all singular K-polystable limits of these Fano threefolds are also divisors in
![](https://chart.googleapis.com/chart?cht=tx&chl=%24(%5Cmathbb%7BP%7D%5E1)%5E4%24&chf=bg,s,333333&chco=ffffff)
of degree
![](https://chart.googleapis.com/chart?cht=tx&chl=%24(1%2C1%2C1%2C1)%24&chf=bg,s,333333&chco=ffffff)
, and the corresponding K-moduli space can be obtained as a natural GIT quotient, which is classically known (but not well known) to be isomorphic to the weighted projective space
![](https://chart.googleapis.com/chart?cht=tx&chl=%24%5Cmathbb%7BP%7D(1%2C3%2C4%2C6)%24&chf=bg,s,333333&chco=ffffff)
. Surprisingly, this is not the case - some singular K-polystable limits of smooth Fano threefolds of Picard rank 4 and degree 24 are not divisors in
![](https://chart.googleapis.com/chart?cht=tx&chl=%24(%5Cmathbb%7BP%7D%5E1)%5E4%24&chf=bg,s,333333&chco=ffffff)
of degree
![](https://chart.googleapis.com/chart?cht=tx&chl=%24(1%2C1%2C1%2C1)%24&chf=bg,s,333333&chco=ffffff)
. In this talk, I will find all singular K-polystable limits of smooth Fano threefolds of Picard rank 4 and degree 24, and show that the corresponding K-moduli space is a weighted blow up of
![](https://chart.googleapis.com/chart?cht=tx&chl=%24%5Cmathbb%7BP%7D(1%2C3%2C4%2C6)%24&chf=bg,s,333333&chco=ffffff)
at a smooth point with weights
![](https://chart.googleapis.com/chart?cht=tx&chl=%24(1%2C2%2C3)%24&chf=bg,s,333333&chco=ffffff)
. This is a joint work with Maksym Fedorchuk (Boston), Kento Fujita (Osaka) and Anne-Sophie Kaloghiros (London).
Link information
Zoom ID:838 7836 1163
passcode:714285
Organizer: Jungkai Chen (NTU)