I am trying to study the proof of this result. It appears as part 3 of the proposition on page 2 of the following document http://math.mit.edu/classes/18.721/projgeom6.pdf I understand everything but the last line. Here the author says $\psi_{\lambda}(P_i)=P_j$ for all nonzero $\lambda$ implies $\psi_{\lambda}(P_i)=P_i$. I would appreciate if anyone can throw some insight on this. Thanks
minimal primes of a homogeneous ideal are homogeneous
5
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commutative-algebra