On the set of divisors with zero geometric defect

Abstract

Abstract Let f : ℂ → X {f:\mathbb{C}\to X} be a transcendental holomorphic curve into a complex projective manifold X. Let L be a very ample line bundle on X . {X.} Let s be a very generic holomorphic section of L and D the zero divisor given by s . {s.} We prove that the geometric defect of D (defect of truncation 1) with respect to f is zero. We also prove that f almost misses general enough analytic subsets on X of codimension 2.