Kollár and Kovács's Question on Cohomology of Fibers
Kollár and Kovács asked whether the first cohomology of the structure sheaf of the fibers must be constant for a flat projective morphism to a smooth curve whose fibers are Cohen-Macaulay and reduced and whose generic fiber is smooth. It need not be: such a morphism exists with non-constant first cohomology.
- Result
- Disproved
- Status
- Resolved
- AI contribution
- AI-discovered
- Method
- Construction
- Field
- Algebraic geometry
- Posed by
- János Kollár, Sándor Kovács
- Year posed
- —
- Years open
- —
- Solved
- 2026-05-20
- Model
- ChatGPT 5.5 Pro and Rethlas
- Vendor
- —
- Collaborators
- Jihao Liu
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 20 / 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. As in the companion notes, the disclosure is a single sentence and does not separate the two systems' contributions.
Verification
The answer is an explicit morphism, so it reduces to verifying the stated properties of that construction. arXiv preprint, not peer-reviewed.