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so previously given a complete linear system d on a complex number surface x we looked at the homomorphic map corresponding to the affinity and we asked what is a criterion for vd to be an embedding was a sufficient and accessory criterion for feed to be an embedding and in the previous video we have given a criterion for fidi to be injective in terms of the riemann rock spaces remember we want to rephrase everything about the mfid in terms of rumor rock spaces so that we can use tools from linear algebra however thatamp;#39;s not the end of the story yet thatamp;#39;s why we have this video because it turns out that injectivity does not implies being an embedding in particular so what it means is being injective on points doesnamp;#39;t imply being injected on tangent spaces necessarily letamp;#39;s look at an example letamp;#39;s look at the following injective map on the riemann sphere from the compact human surface which is a rheumatosphere to p2 now we will write it in terms
