Weakly special varieties, Campana stacks, and Remarks on Orbifold Mordell
Finn Bartsch, Ariyan Javanpeykar

TL;DR
The paper constructs novel weakly special surfaces not Campana-special, explores their integral points, and introduces Campana stacks to generalize the concept of root stacks for C-pairs.
Contribution
It presents the first examples of such surfaces, links their integral points to Campana's Orbifold Mordell conjecture, and introduces Campana stacks for parametrizing morphisms of C-pairs.
Findings
Constructed weakly special surfaces not Campana-special.
Proved non-density of integral points relates to Orbifold Mordell conjecture.
Introduced Campana stacks to encode morphisms of C-pairs.
Abstract
We construct the first weakly special surfaces that are not Campana-special, including the complement of the plane curve in . We prove that the set of -integral points on this surface is non-dense for every number field and finite set of finite places of if and only if Campana's Orbifold Mordell conjecture holds for . This basic example carries a natural -action, and the quotient stack is an Artin stack parametrizing points on a C-pair. This leads to the introduction of ``Campana stacks'', which encode morphisms of C-pairs in a manner analogous to the role of root stacks for integral points satisfying prescribed divisibility conditions.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
