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Entire holomorphic curves into projective spaces intersecting a generic hypersurface of high degree

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Xie,  Song-Yan
Max Planck Institute for Mathematics, Max Planck Society;

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引用

Huynh, D. T., Vu, D.-V., & Xie, S.-Y. (2019). Entire holomorphic curves into projective spaces intersecting a generic hypersurface of high degree. Annales de l'Institut Fourier, 69(2), 653-671.


引用: https://hdl.handle.net/21.11116/0000-0004-992D-E
要旨
In this note, we establish the following Second Main Theorem type estimate for every entire non-algebraically degenerate holomorphic curve
$f\colon\mathbb{C}\rightarrow\mathbb{P}^n(\mathbb{C})$, in present of a {\slgeneric} hypersuface $D\subset\mathbb{P}^n(\mathbb{C})$ of sufficiently high degree $d\geq 15(5n+1)n^n$: \[ T_f(r) \leq \,N_f^{[1]}(r,D) + O\big(\log T_f(r)
+ \log r \big)\parallel, \] where $T_f(r)$ and $N_f^{[1]}(r,D)$ stand for the order function and the $1$-truncated counting function in Nevanlinna theory. This inequality quantifies recent results on the logarithmic Green-Griffiths
conjecture.