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We prove that the Fano variety of lines of a cuspidal cyclic cubic fourfoldis a symplectic variety with transversal A2-singularities and we study theproperties of the nonsymplectic order three automorphism induced by thecovering automorphism on the irreducible holomorphic symplectic manifoldobtained by blowing up the singular locus.

The Fano variety of lines of a cuspidal cyclic cubic fourfold