Additional exercises

1. Why is the class of $[Z(s)]$$[Z(s)]$ independent of choice of generic section?
2. Show that for the line bundle $O(-n)$$O(-n)$ the trivialising section 1 on the $z$$z$-disc on the left glues to

the section $w^{-n}$$w^{-n}$ on the $w$$w$-disc on the right

Interpret in terms of zeros and poles!

1. Suppose that $Z\subset M$$Z\subset M$ is a codimension-r submanifold with normal bundle $N$$N$, and assume everything is compact and oriented. Let $[Z]\in H*(M)$$[Z]\in H*(M)$ denote the fundamental class of $Z$$Z$. Show that its self-intersection $[Z].[Z]$$[Z].[Z]$ is (the pushforward from $Z$$Z$ of the Poincare' dual of) $c_{r}(N)$$c_{r}(N)$.