Lemma 33.45.4 (0BEQ)—The Stacks project

Loading [MathJax]/extensions/TeX/mathchoice.js

Lemma 33.45.4. In the situation of Definition 33.45.3 the intersection number $(\mathcal{L}_1 \cdots \mathcal{L}_ d \cdot Z)$ is an integer.

Proof. Any numerical polynomial of degree $e$ in $n_1, \ldots , n_ d$ can be written uniquely as a $\mathbf{Z}$ -linear combination of the functions ${n_1 \choose k_1}{n_2 \choose k_2} \ldots {n_ d \choose k_ d}$ with $k_1 + \ldots + k_ d \leq e$ . Apply this with $e = d$ . Left as an exercise. $\square$

Comments (0)

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$ ). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).

Comments (0)

Post a comment