Work

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

Year: 2026

Type: article

Abstract: We prove Vojta’s abc conjecture for the projective space P n ⁢ ( C ) \mathbb{P}^{n}(\mathbb{C}) , assuming that the entire curves in P n ⁢ ( C ) \mathbb{P}^{n}(\mathbb{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 n=2 (see [J. Guo and J. T.-Y. Wang, A complex case of Vojta’s general ABC conjecture and cases of Campana’s orbifold conjecture, Trans. Amer. Math. Soc. 377 (2024), 7, 4961–4991]). 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.

Source: Journal für die reine und angewandte Mathematik (Crelles Journal)

DOI: 10.1515/crelle-2026-0020

Authors: Min Ru, Julie Tzu-Yueh Wang

Institutions: University of Houston, Institute of Mathematics, Academia Sinica, Academia Sinica

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science and Technology Council, Simons Foundation

Awards: Diophantine Approximation and Nenvanlinna Theory for Subvarieties, G2291820885, G5254592954