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Duality for relative Prymians associated to K3 double covers of del Pezzo surfaces of degree 2

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Abstract

Markushevich and Tikhomirov provided a construction of an irreducible symplectic V-manifold of dimension 4, the relative compactified Prym variety of a family of curves with involution, which is a Lagrangian fibration with polarization of type (1,2). We give a characterization of the dual Lagrangian fibration. We also identify the moduli space of Lagrangian fibrations of this type and show that the duality defines a rational involution on it.

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Acknowledgments

I would like to thank Dimitri Markushevich for his help.

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  1. Departement of Mathematics, Lille 1 University, 59655 , Villeneuve d’Ascq, France

    Grgoire Menet

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  1. Grgoire Menet
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Correspondence to Grgoire Menet.

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Menet, G. Duality for relative Prymians associated to K3 double covers of del Pezzo surfaces of degree 2. Math. Z. 277, 893–907 (2014). https://doi.org/10.1007/s00209-014-1283-9

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  • DOI: https://doi.org/10.1007/s00209-014-1283-9

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