Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

When we say, that, say, a surface contains ${\infty}^{k}$ lines, do we mean that it contains a k-parameter family of lines? Do we assume that this family is parametrized by a $P^{k}$, say, or we use this term more informally? This is certainly a standard notation, but I didn't see its explanation in standard modern textbooks.

share|improve this question
    
I have never seen the notation $\infty^k$ in algebraic geometry. Could you provide a reference? –  Pete L. Clark Mar 16 '10 at 14:26
3  
@Pete: Arbarello, Cornalba, Griffiths and Harris, page 13. –  Alberto García-Raboso Mar 16 '10 at 14:54

1 Answer 1

up vote 3 down vote accepted

The terminology is fairly common in classical works on projective algebraic/differential geometry. I am not aware of its origins. Anyway it is used rather informally and only means that you have a $k$-dimensional "continuous" family of objects. The parameter space usually is only local and should be thought as a small ball in $\mathbb C^k$.

share|improve this answer
    
Thank you, Jorge. –  rat Mar 16 '10 at 18:40
    
You are welcome, rat. –  jvp Mar 16 '10 at 19:58

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.