There exist two families of complex Coble surfaces with irreducible boundary C such that the automorphism T satisfies T restricted to C is the identity; the first family is nodal with T the identity on the whole surface, and the second has codimension 3 in the moduli space.
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On Coble surfaces and their automorphisms
There exist two families of complex Coble surfaces with irreducible boundary C such that the automorphism T satisfies T restricted to C is the identity; the first family is nodal with T the identity on the whole surface, and the second has codimension 3 in the moduli space.