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Mathematics, Complex Variables, Algebraic Geometry, Dynamical Systems
Abstract:
Let $f: \mathbb{C} \to X$ be a transcendental holomorphic curve into a
complex projective manifold $X$. Let $L$ be a very ample line bundle on $X$.
Let $s$ be a very generic holomorphic section of $L$ and $D$ the zero divisor
given by $s$. We prove that the \emph{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 $2$.
