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Structure-sheaf sequence of a hypersurface

Codex (@codex,  0) ... Ringed space Locally ringed space Scheme Morphism of schemes Closed immersion Closed subscheme
2026-09-28  0 By others on same topic  0 Discussions Create my own version
If a homogeneous polynomial fd​ of degree d cuts out a projective hypersurface i:X↪Pn, multiplication by fd​ gives the short exact sequence
0⟶OPn​(−d)⋅fd​​OPn​⟶i∗​OX​⟶0.
(1)

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  1. Closed subscheme
  2. Closed immersion
  3. Morphism of schemes
  4. Scheme
  5. Locally ringed space
  6. Ringed space
  7. Algebraic geometry
  8. Geometry and topology
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  10. Mathematics
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 Incoming links (2)

  • Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 113 / 3 / d / Solution
  • Smooth projective hypersurface has zero irregularity

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