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

Let X be a nice projective variety (say, smooth and defined over the complex numbers) embedded in some projective space, and let $F:X\to\mathbb{P}^n$ be a rational map given by $[f_0:f_1:\cdots: f_n]$ where the $f_i$ are coprime homogeneous polynomials of degree d (of course, there is just one way to choose them satisfying this, up to constants factors). Consider H the hyperplane divisor $\mathbb{P}^n$, and H' the hyperplane divisor on X. It seems that F*(H)=dH', at least in this case. I have two questions about this situation; (1)What is the name of this number? I couldn't find it anywhere. (2)What is the relation between this number and the degree of the map when F is finite (if any)? One may think they are the same but the Segre embedding shows that this is not the case. Thanks in advance.

share|improve this question
add comment

Your Answer

 
discard

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

Browse other questions tagged or ask your own question.