We show that the number of lines in an $m$--homogeneous supersolvable line arrangement is upper bounded by $3m-3$ and we classify the $m$--homogeneous supersolvable line arrangements with two modular points up-to lattice-isotopy. A lower bound for the number of double points $n_2$ in an $m$--homogeneous supersolvable line arrangement of $d$ lines is also considered. When $3 \leq m \leq 5$, or when $m \geq \frac{d}{2}$, or when there are at least two modular points, we show that $n_2 \geq \frac{d}{2}$, as conjectured by B. Anzis and S. O. Toh\u aneanu. This conjecture is shown to hold also for supersolvable line arrangements obtained as cones over generic line arrangements, or cones over arbitrary line arrangements having a generic vertex.

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关于复杂的超可解线排列

我们表明 $m$--均质超可解线排列中的线数上限为 $3m-3$，我们将 $m$--均质超可解线排列分类为具有两个模块化点直至晶格同位素. 还考虑了 $m$--$d$ 线的齐次超可解线排列中双点 $n_2$ 的数量的下限。当 $3 \leq m \leq 5$，或当 $m \geq \frac{d}{2}$，或当至少有两个模点时，我们证明 $n_2 \geq \frac{d}{2 }$，由 B. Anzis 和 SO Toh\u aneanu 推测。该猜想也适用于作为通用线排列上的锥体或具有通用顶点的任意线排列上的锥体获得的超可解线排列。