Campana's orbifold conjecture for numerically equivalent divisors
Complex Variables
2025-06-03 v1 Algebraic Geometry
Abstract
We prove the following version of the Campana's orbifold conjecture: Let be a complex non-singular projective variety of dimension . Let be -linearly independent effective divisors in and be a normal crossing divisor of . Assume furthermore that they are numerically parallel. Let and let be an orbifold entire curve. Then, there exists a positive integer such that, the orbifold is of general type, where , and if has multiplicity at least along , , then must be algebraically degenerate.
Cite
@article{arxiv.2506.00873,
title = {Campana's orbifold conjecture for numerically equivalent divisors},
author = {Min Ru and Julie Tzu-Yueh Wang},
journal= {arXiv preprint arXiv:2506.00873},
year = {2025}
}