Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I hear sometimes about a generic hyperplane of a projective space over $\mathbb{C}$, for example in the Noether-Lefschetz theorem. What is the definition of it?

share|improve this question

1 Answer 1

Saying that something is true for a generic hyperplane in $\mathbf P^n$ is saying that it's true for all hyperplanes outside of a proper subvariety of the space of hyperplanes (which is also a projective space of dimension $n$). I think it can also mean, more generally, for all hyperplanes outside of a countable union of proper subvarieties.

share|improve this answer

Your Answer

 
discard

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

Not the answer you're looking for? Browse other questions tagged or ask your own question.