The algebraic Green-Griffiths-Lang conjecture for complements of very general pairs of divisors
Abstract
We prove that the complement of a very general pair of hypersurfaces of total degree $2n$ in $\mathbb{P}^n$ is algebraically hyperbolic modulo a proper closed subvariety. This provides evidence towards conjectures of Lang-Vojta and Green-Griffiths, and partially extends previous work of Chen, Pacienza-Rousseau, and Chen-Riedl and the third author.
- Publication:
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arXiv e-prints
- Pub Date:
- October 2024
- DOI:
- 10.48550/arXiv.2410.00640
- arXiv:
- arXiv:2410.00640
- Bibcode:
- 2024arXiv241000640A
- Keywords:
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- Mathematics - Algebraic Geometry;
- Mathematics - Number Theory;
- 14J70;
- 14C20;
- 32Q45
- E-Print:
- 14 pages, comments welcome!