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Here we study zero-dimensional subschemes of ruled varieties, mainly Hirzebruch surfaces and rational normal scrolls, by applying the Horace method and the Terracini method
Let be a bounded strictly pseudoconvex domain in and let be a positive divisor of with finite area. We prove that there exists a bounded holomorphic function such that is the zero set of . This result has previously been obtained by Berndtsson in the case where is the unit ball in .
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