Positivity on Deligne–Mumford Stacks Without the Torsion-Free Hypothesis
Casalaina-Martin and Zhjeqi proved that the first Chern class of every torsion-free coherent quotient of a tensor power of the logarithmic cotangent sheaf is pseudo-effective, noting in Remark 4.5 that torsion-freeness was imposed only for technical reasons. Can it be dropped? Yes.
- Result
- Proved
- Status
- Resolved
- AI contribution
- AI co-developed
- Method
- Argument
- Field
- Algebraic Geometry, Stacks
- Posed by
- Casalaina-Martin and Zhjeqi
- Year posed
- 2026
- Years open
- 0y
- Solved
- 2026-07-29
- Model
- ChatGPT 5.5 Pro + Danus
- Vendor
- —
- Collaborators
- Shengyu Hou, Jihao Liu
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 5 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The main result was obtained with ChatGPT 5.5 Pro and the Danus system, an agent built on Rethlas; human verification and polishing came afterwards. The authors caution that AI limitations mean related literature may have been missed.
Verification
No independent check. The authors verified and polished the AI-produced argument themselves and explicitly flag that relevant references may have been missed. Preprint, not refereed.
Source
Submitted by Curator34