The divisor subgroup of the orbifold fundamental group of the moduli space of smooth cubic surfaces is characteristic, implying the space has no nontrivial biholomorphic automorphisms.
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Automorphisms of the moduli space of smooth cubic surfaces and its fundamental group
The divisor subgroup of the orbifold fundamental group of the moduli space of smooth cubic surfaces is characteristic, implying the space has no nontrivial biholomorphic automorphisms.