When speaking of a sheaf $E$ on a complex surface $X$, if an author writes
should I understand this to really mean
$$\int_X ch_2(E) < \int_X c_1(E)\wedge c_1(E)?$$
Because I think of chern characters and chern classes as living in $H^\bullet(X,Q)$ and $H^\bullet(X,Z)$ respectively, I don't know how else to interpret the inequality.
I apologize ahead of time for this naive question, as I'm new to algebraic geometry.