1. Why is the class of ${\displaystyle [Z(s)]}$ independent of choice of generic section?
2. Show that for the line bundle ${\displaystyle O(-n)}$ the trivialising section 1 on the ${\displaystyle z}$-disc on the left glues to
the section ${\displaystyle w^{-n}}$ on the ${\displaystyle w}$-disc on the right
1. Suppose that ${\displaystyle Z\subset M}$ is a codimension-r submanifold with normal bundle ${\displaystyle N}$, and assume everything is compact and oriented. Let ${\displaystyle [Z]\in H*(M)}$ denote the fundamental class of ${\displaystyle Z}$. Show that its self-intersection ${\displaystyle [Z].[Z]}$ is (the pushforward from ${\displaystyle Z}$ of the Poincare' dual of) ${\displaystyle c_{r}(N)}$.