Vojta's abc conjecture for entire curves in toric varieties highly ramified over the boundary

Min Ru; Julie Tzu-Yueh Wang

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arXiv · 2410.19395

Vojta's abc conjecture for entire curves in toric varieties highly ramified over the boundary

Min Ru·Julie Tzu-Yueh Wang

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Abstract

We prove Vojta's abc conjecture for projective space ${\Bbb P}^n({\Bbb C})$, assuming that the entire curves in ${\Bbb P}^n({\Bbb C})$ are highly ramified over the coordinate hyperplanes. This extends the results of Guo Ji and the second-named author for the case $n=2$ (see \cite{GW22}). We also explore the corresponding results for projective toric varieties. Consequently, we establish a version of Campana's orbifold conjecture for finite coverings of projective toric varieties.

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Min Ru, Julie Tzu-Yueh Wang. 2024-10-25. Vojta's abc conjecture for entire curves in toric varieties highly ramified over the boundary. https://arxiv.org/abs/2410.19395

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