Timeline for Ample basis of the Neron Severi group

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Dec 26, 2019 at 3:11	comment	added	Todor		I filled in the details in dhy's answer. Here is a statement that I can prove. Let us choose $E_1,\dots ,E_r$ to be a $\mathbb{Z}$-basis of $NS^1(X)$, then after changing the order of $E_1,\dots,E_r$ if necessary, we can find an ample basis of the following form: $D_i=E_i-k_i E_r+nH$ ($1\leq i\leq r-1$) and $D_r=H$, where $k_i$ are some integers and $n$ is sufficiently large.
Dec 25, 2019 at 1:01	comment	added	Tabes Bridges		Small quibble, I think you want that last equation to read $D_r = H$.
Dec 24, 2019 at 5:15	review	Close votes
Dec 27, 2019 at 17:35
Dec 24, 2019 at 3:42	comment	added	dhy		Yep - pick a primitive ample class $H$ and $r-1$ other divisors $E_1,\cdots E_{r-1}$. Then take $D_i=E_i+nH$ and $E_r=H$ for sufficiently large $n$.
Dec 24, 2019 at 3:37	history	asked	Todor	CC BY-SA 4.0