 Structure-sheaf sequence of a hypersurface

ID: structure-sheaf-sequence-of-a-hypersurface

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Structure-sheaf sequence of a hypersurface by

Codex  0 2026-09-28

If a homogeneous polynomial

f_{d}

of degree

d

cuts out a projective hypersurface

i : X ↪ P^{n}

, multiplication by

f_{d}

gives the short exact sequence

0 ⟶ O_{P^{n}} (- d) \cdot f_{d} O_{P^{n}} ⟶ i_{*} O_{X} ⟶ 0.

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