Local negativity of surfaces with non-negative Koidara dimension and   transversal configurations of curves
  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 $X \subset \mathbb{P}^{n+2}_{\mathbb{C}}$ of multi-degree $d=(d_1, \dots, d_n)$, and we provide a sharp and uniform bound on their H-constants, which only depends on $d$. 
Roberto Laface, Piotr Pokora
math.AG