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Mar 1, 2020 at 10:48 vote accept user130022
Feb 16, 2020 at 10:43 comment added user130022 Sorry I got the answer. Probably we can move the point in the 2nd plane or in 1st plane to get that generality hypothesis. thanks.
Feb 16, 2020 at 10:41 comment added user130022 Can we impose that generality assumption from the generality assumption on points in the plain ? sorry for bothering you again
Feb 16, 2020 at 10:37 comment added user130022 Now i have understood. Thank you very much.
Feb 16, 2020 at 10:32 comment added Sasha Assume for simplicity that the pencil has no conics containing $L$. Then $t \mapsto C'_t \cap L$ defines a map $\mathbb{P}^1 \to S^2L = \mathbb{P}^2$ (its image is, in fact, a line). On the other hand $C'' \cap L$ defines a point of $S^2L$. So, the extra generality assumption that you need is that the above line in $S^2L$ does not contain the above point.
Feb 16, 2020 at 10:26 comment added user130022 Thank you very much for the answer. I have a silly question: why there is no $t$ such that (*) hols ?
Feb 16, 2020 at 9:43 history answered Sasha CC BY-SA 4.0