K-moduli of Fano 3-folds can have embedded points

Abstract

We exhibit an example of obstructed K-polystable Fano 3-fold $X$ such that the K-moduli stack of K-semistable Fano varieties and the K-moduli space of K-polystable Fano varieties have an embedded point at $[X]$.

12 pages, 4 figures. v2: corrected an error in Sec.5, made small adjustments. Will appear in the EMS Volume "Varieties, polyhedra and algorithms"