Lemma 55.9.7. In Situation 55.9.3 the symmetric bilinear form (55.9.6.1) has the following properties
(C_ i \cdot C_ j) \geq 0 if i \not= j with equality if and only if C_ i \cap C_ j = \emptyset ,
(\sum m_ i C_ i \cdot C_ j) = 0,
there is no nonempty proper subset I \subset \{ 1, \ldots , n\} such that (C_ i \cdot C_ j) = 0 for i \in I, j \not\in I.
(\sum a_ i C_ i \cdot \sum a_ i C_ i) \leq 0 with equality if and only if there exists a q \in \mathbf{Q} such that a_ i = qm_ i for i = 1, \ldots , n,
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