K-moduli of curves on a quadric surface and K3 surfaces

Kenneth Ascher, Kristin DeVleming, Yuchen Liu

We show that the K-moduli spaces of log Fano pairs $({\mathbb{P}}^1\times {\mathbb{P}}^1,cC)$ where $C$ is a $(4,4)$-curve and their wall crossings coincide with the VGIT quotients of…