Abstract
AbstractThe 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 the perfect cone compactification of the quotient of the type IV domain $$D_{L}$$
D
L
associated to an even lattice L. In our main theorem we show that the pair $${ (\overline{D_{L}/\widetilde{O}^{+}(L)}^{p}, \Delta /2) }$$
(
D
L
/
O
~
+
(
L
)
¯
p
,
Δ
/
2
)
has klt singularities, where $$\Delta $$
Δ
is the closure of the branch divisor of $${ D_{L}/\widetilde{O}^{+}(L) }$$
D
L
/
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.
Publisher
Springer Science and Business Media LLC
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