Problem detail · source-aware
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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.
The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.
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.
Provider: unknown · Prompt public: unknown · Independence: unknown
No independent check. The answer is an explicit morphism, so it reduces to verifying the stated properties of that construction. arXiv preprint, not peer-reviewed.
Correctness: unknown · statement fidelity: unaudited · peer review: none
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Source-reported tools: construction.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.