The perfect cone compactification is a toroidal compactification which can be defined for locally symmetric varieties. Let $$\overline{D_{L}/\widetilde{O}^{+}(L)}^{p}$$ D L / O ~ + ( L ) ¯ p be… Click to show full abstract
The perfect cone compactification is a toroidal compactification which can be defined for locally symmetric varieties. Let $$\overline{D_{L}/\widetilde{O}^{+}(L)}^{p}$$DL/O~+(L)¯p be the perfect cone compactification of the quotient of the type IV domain $$D_{L}$$DL associated to an even lattice L. In our main theorem we show that the pair $${ (\overline{D_{L}/\widetilde{O}^{+}(L)}^{p}, \Delta /2) }$$(DL/O~+(L)¯p,Δ/2) has klt singularities, where $$\Delta $$Δ is the closure of the branch divisor of $${ D_{L}/\widetilde{O}^{+}(L) }$$DL/O~+(L). In particular this applies to the perfect cone compactification of the moduli space of 2d-polarised K3 surfaces with ADE singularities when d is square-free.
