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

For a real algebraic variety, is the integral of the product of the Chern classes of two line bundles equal to the intersection number of the two corresponding divisors?

share|improve this question
add comment

1 Answer 1

up vote 3 down vote accepted

I'm not sure what you mean by a line bundle on a real algebraic variety and its Chern classes, but for smooth complex analytic manifolds the Chern class of a line bundle corresponding to a divisor is Poincare dual to the homological class of the divisor, as explained e.g. in Griffiths-Harris, Chapter 1, Chern classes of line bundles. So the $c_2([D_1]\oplus [D_2])=c_1[D_1]c_1[D_2]$ is indeed the indeed Poincare dual to the intersection class of $D_1$ and $D_2$. If the manifold is a surface, then we get the a number.

Maybe this not what you meant, but in that case you should really add some more details to your question.

share|improve this answer
So in the case of a surface these two numbers should coincide, right? –  Jean Delinez Jan 28 '10 at 23:50
Jean -- yes, for smooth complex analytic surfaces they coincide. –  algori Jan 28 '10 at 23:58
add comment

Your Answer


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.