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As for the definition of an analytic family parametrized by a complex analytic space, we follow Kuranishi [2]. Similar extension problem has recently been treated by Ph. A, Griffiths (Proceedings of the Conference on complex analysis, Minneapolis 1964), and the author was influenced by his work. But our result is not covered by his, and the author thinks it suitable to give here a presentation independent of his. Our treatment goes along the line of Nakano [4].

Extension problem of complex line bundles for Kähler surfaces