A projective complete intersection defined by a regular sequence in a polynomial ring has pure codimension equal to the sequence length and has no embedded associated primes. Thus its components account for the whole degree, with their generic multiplicities. This fact excludes hidden embedded points when a contained curve already has the full intersection degree.

Ancestors (12)

  1. Projective complete intersection
  2. Closed subscheme
  3. Closed immersion
  4. Morphism of schemes
  5. Scheme
  6. Locally ringed space
  7. Ringed space
  8. Algebraic geometry
  9. Geometry and topology
  10. Area of mathematics
  11. Mathematics
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