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

of degree

. 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

of degree

, 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

. 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

of degree

. 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

at a smooth point with weights

. 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)