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 $X$ be a smooth variety over $\mathbb{C}$. Blowing up a subvariety $Y\subset X$ of codimension $\ge 2$, we get $\pi: X'\rightarrow X$. Assume $X'$ is smooth and $E$ is the only exceptional divisor.

Let $C\subset E$, but not contracted by $\pi$, i.e. $\pi(C)$ is still a curve. What can we say about the intersection number $C. E$?

share|cite|improve this question

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.