= Projection formula for algebraic cycles
{title2=$f_*(f^*D\cdot\alpha)=D\cdot f_*\alpha$}
For a proper <morphism of varieties> $f:X\to Y$, a <Cartier divisor> $D$ on $Y$, and an <algebraic cycle> $\alpha$ on $X$, pullback of $D$, intersection with $\alpha$, and proper pushforward satisfy the displayed identity in the <Chow group>. In particular, for a <generically finite morphism> of surfaces of degree $r$, $(f^*D)^2=rD^2$. For a curve $C$ contracted to a point, $f_*C=0$, so $f^*D\cdot C=0$.
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