In this note we consider the blowing-up X of P3 along r general points of the anticanonical divisor of a smooth quadric in P3. Given a complete linear system ? = dH - mE - - mrEr | on X, with H the pull-back of a plane in P3 and Ei the exceptional divisor corresponding to Pi, we give necessary and sufficient conditions for the very ampleness (resp. base point freeness and non-speciality) of C. As a corollary we obtain a sufficient condition for the very ampleness of such a complete linear system on the blowing-up of P3 along r general points.
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机译：在本说明中，我们考虑P3的P3吹出x沿着P3中光滑Quadicric的抗致谐波除数的一般点。给定完整的线性系统？ = dh - m e - - erer |在x上，用p3和ei的平面拉回与pi对应的异常除数，我们为c的非常放大（resp point freeness和非专业）给出了必要和充分的条件。作为推论我们获得了足够的条件，以便在沿R一般点吹出P3的爆炸上的这种完整的线性系统的非常显着的条件。
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