Hi folkz,

I'm trying to learn more about line bundles, invertible sheaves and divisors on schemes. I understand the connection beweteen Cartier and Weil Divisors and the connection between Cartier Divisors and invertible sheaves and how to get from one to another (as far as possible).

But compared to my analytic imagination of a line bundle I don't see how to come from an invertible sheaf to the line bundle (apart from the fact, that these two terms coincide).
Where is '*the line*' in my locally free of rank one $\mathcal{O}_X$-module?

greatz Johannes