K moduli of log del Pezzo pairs

Fei Si; Haoyu Wu; Long Pan

arxiv: 2303.05651 · v2 · pith:MAASWSKFnew · submitted 2023-03-10 · 🧮 math.AG

K moduli of log del Pezzo pairs

Long Pan , Fei Si , Haoyu Wu This is my paper

classification 🧮 math.AG

keywords oplusk-modulioverlinepairspezzospacesassociatedcoincide

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We establish the full explicit wall-crossing for K-moduli space $\overline{P}^K_c$ 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 $\overline{P}^K_c$ coincide with Hassett-Keel-Looijenga(HKL) models $\cF(s)$ of a $18$-dimensional locally symmetric spaces associated to the lattice $E_8\oplus U^2\oplus E_7\oplus A_1$.

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