I was reading wikipedia page on intersection theory, and it says that one can define self-intersection of a curve, and sometimes the number is negative. In the case there is a small deformation of the curve, say C' is a small deformation of C, one can define C.C=C.C', and this is quite intuitive. However, if the curve is an exceptional divisor of a blowup, there is no small deformation and I can't quite imagine geometrically how the self-intersection can be negative. Any idea?
Also, does anyone know a reference to Castelnuovo's contraction theorem that any (-1)-curve can be contracted?