In Shafarevich´s Example 4.7 in page 244 (Basic Algebraic Geometry), one finds the following.
I have two questions:
1.- Why $\sum k_i deg C_i=m-1$? He defines the degree of a of a projective variety of dimension $n$ as $E^n$, where $E$ is the divisor given by a hyperplane, but I don't see why is this related to the degree of this (or any) $E$.
2.- Why $EL=1$? That $L$ is a line doesn't explain much to me.
Thanks in advance.