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SUMMARY:Products of K-moduli spaces - Theodoros Stylianos Papazachariou (U
 niversity of Cambridge)
DTSTART:20240524T140000Z
DTEND:20240524T150000Z
UID:TALK217075@talks.cam.ac.uk
DESCRIPTION:In recent years\, K-stability has made extraordinary progress 
 in constructing moduli spaces of Fano varieties and log Fano pairs. This c
 onstruction\, however\, is not explicit\, and needs to be studied in a cas
 e-by-case basis to explicitly describe specific examples of moduli spaces 
 for Fano varieties. In this talk I will describe the local and global stru
 ctures of the K-moduli space of products of Fano varieties and provide a m
 ethod to study K-moduli spaces of products of Fano varieties. I will demon
 strate that a connected component of the K-moduli stack that contains a pr
 oduct\, must only contain product Fano varieties. I will also demonstrate 
 that there exists a well-defined morphism from the product of K-moduli sta
 cks of Fano varieties to the K-moduli stack of their product and show that
  it is an isomorphism under specific conditions. Using this I will present
  some explicit examples of reduced connected components of the K-moduli st
 ack of Fano threefolds\, and log Fano pairs.
LOCATION:Seminar Room 2\, Newton Institute
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