cartier divisor - very ample divisor : 2024-11-01 cartier divisorAs a basic result of the (big) Cartier divisor, there is a result called Kodaira's lemma:Let X be a irreducible projective variety and let D be a big Cartier divisor on X and let H be an arbitrary effective Cartier divisor on X. Then See more
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cartier divisorLet X be an integral Noetherian scheme. Then X has a sheaf of rational functions $${\displaystyle {\mathcal {M}}_{X}.}$$ All regular functions are rational functions, which leads to a short exact sequenceA Cartier divisor on . See moreAs a basic result of the (big) Cartier divisor, there is a result called Kodaira's lemma:Let X be a irreducible projective variety and let D be a big Cartier divisor on X and let H be an arbitrary effective Cartier divisor on X. Then See more
cartier divisorvery ample divisorLet φ : X → Y be a morphism of integral locally Noetherian schemes. It is often—but not always—possible to use φ to transfer a divisor D from one scheme to the other. Whether this is possible depends on whether the divisor is a Weil or Cartier divisor, . See moreFor an integral Noetherian scheme X, the natural homomorphism from the group of Cartier divisors to that of Weil divisors gives a homomorphism$${\displaystyle c_{1}:\operatorname {Pic} (X)\to \operatorname {Cl} (X),}$$known as the first See more
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cartier divisor