David Dynerman
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Registered User
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Graduate Student
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Apr 6 |
comment |
Why does the naive choice of homogeneous coordinate ring of a product of projective schemes not work? It's helpful to remember that a graded ring S gives not only a projective scheme but also an embedding (via S(1)), and lots of rings can give the same projective scheme. If S is the ring you cite from Hartshorne, then S(1) gives the Segre embedding of your projective variety. I'm also interested in knowing if there are other easy rings to write down whose Proj gives you X x X. In the case when S is the polynomial ring k[x,y], then the total tensor product just gives you k[x,y,z,w], so you just get P^3 which isn't what we want. |
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Feb 15 |
awarded | ● Great Question |
