F-theory with hyperelliptic fibrations

A bstract We discuss the role of hyperelliptic fibrations in F-theory. For each even integer n we give a noncompact Calabi-Yau threefold X containing a hyperelliptically fibered surface Y , such that X and Y are homotopy equivalent and c 2 ( X ) = n . We investigate two distinct cases depending on the position of the hyperelliptic fibration. First, we propose to extend F-theory considering hyperelliptic fibrations, giving an identification between the determinant of the period matrix and the axio-dilaton. Such an identification requires that the curve satisfies an appropriate criterium which we describe. Our explicit examples have split Jacobian, preserve the same number of degrees of freedom of usual F-theory while allowing for the appearance of a greater variety of singularities. Second, when the hyperelliptic fibration is contained in the base of a Calabi-Yau fourfold, we show that tadpole cancellation conditions are satisfied for arbitrarily large values of c 2 ( X ).