7
votes
1answer
234 views

Top self-intersection of exceptional divisors

Let $Y\subset\mathbb{P}^n$ be a smooth variety of codimension two. Consider the blow-up $X = Bl_Y\mathbb{P}^n$ of $\mathbb{P}^n$ along $Y$, and let $E$ be the exceptional divisor over $Y$. Then $E$ ...
1
vote
1answer
416 views

Self intersection of blown up points and the lines which they lie on

I'm currently trying to understand the process of blowing-up, and a few things strike me as a little difficult to get an intuitive understanding of what's happening. The current problem is on self ...
2
votes
1answer
556 views

(Anti)Canonical divisor of a blow up

This question may be utterly trivial, or not, but as someone with hardly any knowledge of algebraic geometry I thought there could be a chance I get lucky. Let X be a rational surface obtained by n ...