A generic global Torelli theorem for certain Horikawa surfaces
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© Foundation Compositio Mathematica 2019. Algebraic surfaces of general type with q = 0, p g = 2 and K 2 = 1 were described by Enriques and then studied in more detail by Horikawa. In this paper, we consider a 16-dimensional family of special Horikawa surfaces which are certain bidouble covers of P 2 . The construction is motivated by that of special Kunev surfaces which are counterexamples for the infinitesimal Torelli and generic global Torelli problems. The main result of the paper is a generic global Torelli theorem for special Horikawa surfaces. To prove the theorem, we relate the periods of special Horikawa surfaces to the periods of certain lattice polarized K3 surfaces using eigenperiod maps and then apply a Torelli type result proved by Laza.
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