On the set of divisors with zero geometric defect

preprint2020arXivOpen access

Abstract

Let f:C→Xf: \mathbb{C} \to X be a transcendental holomorphic curve into a complex projective manifold XX. Let LL be a very ample line bundle on XX. Let ss be a very generic holomorphic section of LL and DD the zero divisor given by ss. We prove that the \emph{geometric} defect of DD (defect of truncation 11) with respect to ff is zero. We also prove that ff almost misses general enough analytic subsets on XX of codimension 22.

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