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.

Exact FrontierDelta

Prior state unknown→disproved

Scope and record

Occurred: May 20, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-discovered. Imported under CC BY 4.0.

Canonical aliases: Kollár and Kovács's Question on Cohomology of Fibers · Kollár-Kovács fiber cohomology

Confidence: Not scored

Registry verification: unreviewed · preprint · resolved

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Attribution

VibeMathed
registry · event recorded by

Jihao Liu
human · human collaborator

ChatGPT 5.5 Pro
model · ai model contributor

Rethlas
model · ai model contributor

Lineage and corrections

This event attributed to Jihao Liu

This event attributed to Rethlas

This event attributed to ChatGPT 5.5 Pro

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