Enriques manifolds

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Enriques surfaces comprise one of the four fundamental classes of algebraic surfaces whose tangential bundle is numerically trivial, and is to date subject of intensive research.Recently, the notion of Enriques surfaces was generalized to higher dimensions, with the help of hyperkähler manifolds.In this research project we shall investigate certain arithmetic and geometric properties of Enriques surfaces and Enriques manifolds.One research goal is to determine whether or not special Enriques surfaces are definable by polynomial equations with integral coefficients so that no singularities arise at all finite primes. By results of Fontaine, this is indeed impossible for the related classes of algebraic surfaces.Further goals are to construct new and more complicated examples for Enriques manifolds, and to develop a theory of Enriques manifolds in positive characteristics.