K moduli of log del Pezzo pairs

Abstract

We establish the full explicit wall-crossing for K-moduli space ${\overline{P}}_c^K$ of degree $8$ del Pezzo pairs $(X,cC)$ where generically $X \cong \bbF_1$ and $C\sim -2K_X$. We also show K-moduli spaces ${\overline{P}}_c^K$ coincide with Hassett-Keel-Looijenga(HKL) models $\cF(s)$ of a $18$-dimensional locally symmetric spaces associated to the lattice $E_8\oplus U^2\oplus E_7\oplus A_1$.

43 pages, comments are welcome! Some typos are fixed and the introduction is improved