*First a note of caution:* I am a physicist with a rudimentary knowledge of algebraic geometry picked up here and there. So don't assume I know anything besides basic properties of sheaves and try to give as simple answers as possible. Also, if my questions don't make sense for any reason, try to point me in the right direction.

So, my questions:

I'd like to hear the definition of the

*ample generator of a Picard group*. I know what a Picard group is but I am having a hard time finding an actual definition of its ample generator.Why is this notion important and where is it used primarily?

If you could provide some simple examples to illustrate the notion for some special $X$ and ${\rm Pic}(X)$ that would be welcome.

*Motivation:* recently, Scott Carnahan provided a very nice answer about conformal blocks in CFT over at physics.SE. My problem is that the punchline of his example involves the notion of an ample generator of a Picard group of certain moduli space of $SU(2)$ bundles on the Riemann surface (which is the arena for the CFT).