 Canonical bundle of a smooth projective hypersurface

ID: canonical-bundle-of-a-smooth-projective-hypersurface

For a smooth degree-

d

X_{d} \subset CP^{n}

[X_{d}] ≅ O (d)

give

K_{X_{d}} ≅ (K_{CP^{n}} \otimes [X_{d}]) ∣_{X_{d}} ≅ O_{X_{d}} (d - n - 1) .

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