On the construction of moduli space of Fano varieties with K-stability
-- Chenyang Xu, October 19, 2018

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The project of constructing a moduli space of K-stable Fano varieties aims to find an Artin stack parametrizing K-semistable Fano varieties, which admits a projective good moduli space parametrizing K-polystable Fano varieties. While some parts of the project still remain to be widely open, we want to discuss some recent progress, made by using algebro-geometric method.