# 4 – Proj | AmpTester

Assume known an ample class $a_0 \in S$. Then a class $v\in S$ is ample if and only if the three following conditions all hold.

Condition AC1
$$\langle v, v \rangle_{S} > 0 \quad \text{and} \quad \langle v, a_0 \rangle_{S} >0$$

Condition AC2
$$\{r \in S \mid \langle v,r \rangle_{S} = 0, \; \, \langle r, r\rangle_{S}=-2 \} = \emptyset$$
Checked with ShiChecker

Condition AC3
$$\{ r \in S \mid \langle v, r \rangle_{S} < 0, \;\, \langle a_0 ,r \rangle_{S} >0, \;\, \langle r,r \rangle_{S} =-2 \} = \emptyset$$
Checked with ShiBooster