Weight lemma. (Q2577350)

The author gives a proof for the existence of the weights for hyperplanes in complex projective spaces so called ``Nochka weights''. The Nochka weight (or weight lemma) was introduced by Nochka in 1982. By using his weight lemma, he gave an affirmative answer to Cartan's conjecture. His lemma is very useful and there have been several applications [see e.g., \textit{M. Ru} and \textit{P.-M. Wong}, Invent. Math. 106, No.~1, 195--216 (1991; Zbl 0758.14007)]. However he gave only a sketch of the proof of his results. The first complete proof of the weight lemma was due to \textit{W. Chen} [Trans. Am. Math. Soc. 319, No.~2, 499--515 (1990; Zbl 0701.32013)]. In this paper the author gives the first complete presentation of his original proof with the geometric interpretation of his proof.