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

2024/10/25 by Ru, Min, Wang, Julie Tzu-Yueh · 1 citation
#Complex Variables (math.CV) #FOS: Mathematics #Primary 30D35 #Secondary 32Q45 and 32H30

paper · doi:10.48550/arxiv.2410.19395

Abstract

We prove Vojta's abc conjecture for projective space \Bbb Pⁿ(\Bbb C), assuming that the entire curves in \Bbb Pⁿ(\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 \citeGW22). 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.

Cited by

• Campana's orbifold conjecture for numerically equivalent divisors

Related

• Campana conjecture for coverings of toric varieties over function fields
• Vojta's abc Conjecture for algebraic tori and applications over function fields
• A complex case of Vojta's general abc conjecture and cases of Campana's orbifold conjecture
• Approximating rational points on toric varieties
• Vojta's Conjecture on Multiple Blowups of ℙ² and the abc conjecture