MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Let $X_s = \bigcap_{i=1}^s H_i \subset \mathbb{P}^N$ be a complete intersection, where each $H_i$ is a hypersurface of degree $d_i$.

Is $X_{s-1}$ also a complete intersection? Is the conormal sheaf of $X_s$ in $X_{s-1}$ isomorphic to $\mathcal{O}_{X_s}(-d_s)$?

share|cite|improve this question
Yes for the first question. For the second replace $d_i$ with $d_s$, then the answer is positive as well. – Sasha Dec 14 '12 at 7:33

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.