Study of Algebraic Surfaces is a classical subject. To understand surfaces, it is natural to study the various properties of the curves on them. Even now, there are several interesting conjectures about the properties of curves on surfaces. One such conjecture is the Bounded Negativity Conjecture (BNC).
Let X be a nonsingular projective surface. Bounded Negativity Conjecture (BNC) says that there is an integer b(X), depending only on X, such that the self-intersection C^2 is at least b(X) for every reduced curve C on X. This conjecture is false in positive characteristic, but it is open in characteristic zero, except in trivial cases. Harbourne constants were defined in an attempt to tackle this problem. I will introduce some of these ideas in this talk.
