Primitivity of sublattices generated by classes of curves on an algebraic surface
Ichiro Shimada, Nobuyoshi Takahashi · Rikkyo University academic repository (Rikko Roots) (Rikkyo University) · 2010
Let X be a smooth projective complex surface. Suppose that a finite set of reduced irreducible curves on X is given. We consider the submodule of the second cohomology group of X with integer coefficients generated by the classes of these curves. We present a method to calculate the primitive closure of this submodule, and apply it to cyclic coverings of the projective plane branching along four lines in general position.