MathOverflow will be down for maintenance for approximately 3 hours, starting Monday evening (06/24/2013) at approximately 9:00 PM Eastern time (UTC-4).

4 Title, wording.

# WhydoestheEuler characteristic -----------------------ofatoricvarietyequalthenumberofverticesinthedefiningpolytope?

Hi all

in

In this the following link(http://www.math.leidenuniv.nl/scripties/Trevisan.pdf), , Corollary 3.2.2, page 59 the author claims that: *The Euler characteristic of the toric variety $X_K$ associated to a convex polytope $K$ is the number of vertices of $K$*.K$. I want to see how it works, could some one . Could someone please illustrate this for me by using this method to compute the Euler characteristic of$\mathbb{P}^{2}$and$\mathbb{P}^{1}\times \mathbb{P}^{1}$. thanks mathbb{P}^{1}$? Thanks so much.

3 edited title