The Ciliberto et al. Question on Effective Divisors of Positive Self-Intersection
Ciliberto, Knutsen, Lesieutre, Lozovanu, Miranda, Mustopa and Testa asked a question about effective divisors of positive self-intersection on smooth projective surfaces. The answer is negative, witnessed by a very non-movable effective divisor.
- Result
- Disproved
- Status
- Resolved
- AI contribution
- AI-discovered
- Method
- Construction
- Field
- Algebraic geometry
- Posed by
- Ciro Ciliberto, Andreas Leopold Knutsen, John Lesieutre, Victor Lozovanu, Rick Miranda, Yusuf Mustopa, Damiano Testa
- Year posed
- —
- Years open
- —
- Solved
- 2026-05-20
- Model
- ChatGPT 5.5 Pro and Rethlas
- Vendor
- —
- Collaborators
- Jihao Liu
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 15 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The author states the main result is obtained by generative AI, particularly ChatGPT 5.5 Pro and the Rethlas system. This is the fourth note in a short series where the same author publishes machine-obtained answers to named questions in birational geometry, each with the same one-sentence disclosure.
Verification
The counterexample is an explicit divisor, so it is checkable directly. arXiv preprint, not peer-reviewed.
Source
arXiv:2605.20594 - An example of a very non-movable effective divisor