The double covers of Enrique surfaces are these objects, and in two complex dimensions the only compact simply connected ones are the K3 surfaces.
The double covers of Enrique surfaces are these objects, and in two complex dimensions the only compact simply connected ones are the K3 surfaces. Considering their Hodge numbers gives a derivation of the mirror symmetry, which is equivalent to applying T-duality to their toroidal fibers. Flux-free compactifications over one of these preserve two to the power one minus n supersymmetries, and they contain a nonvanishing harmonic spinor.  These objects have vanishing first real Chern class and a metric with a holonomy contained in SU(n), and one of their namesakes proved that they have Ricci flat metrics. For 10 points, name these mathematical surface, defined as Kahler manifolds with trivial canonical bundles, some of which have the same shape as the extra dimensions of spacetime in string theory, named for two guys.
The double covers of Enrique surfaces are these objects, and in two complex dimensions the only compact simply connected ones are the K3 surfaces.
{Calabi-Yau} manifolds