Let $L$ be the complex line ${ax+by+c=0}$ in $\mathbb{C}^{2}$,and let $C$ be the algebraic curve ${{f(x,y)=0}}$, where $f$ is an irreducible polynomial of degree $d$. Prove that $C\bigcap L$ contains at most $d$ points unless $C=L$.
The intersection of algebraic curves
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algebraic-geometry
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0I guess you're not allowed to use B\'{e}zout's Theorem? – 2012-11-21
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0No, not allowed. – 2012-11-21