Local negativity of surfaces with non-negative Kodaira dimension and transversal configurations of curves

Abstract

We give a bound on the H-constants of configurations of smooth curves having transversal intersection points only on an algebraic surface of non-negative Kodaira dimension. We also study in detail configurations of lines on smooth complete intersections X ⊂Pn+2 C of multi-degree d = (d1, …, dn), and we provide a sharp and uniform bound on their H-constants, which only depends on d.