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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.

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disproveddisproved

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Occurred: Sep 3, 2026

Delta type: REGISTRY REVISION

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

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Registry verification: unreviewed · preprint · resolved

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VibeMathed
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ChatGPT 5.5 Pro
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Rethlas
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Jihao Liu
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Corrects Kollár and Kovács's Question on Cohomology of Fibers

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This event attributed to Rethlas

Kollár and Kovács's Question on Cohomology of Fibers parent of this event

This event attributed to Jihao Liu

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. parent of this event

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VibeMathed record: Kollár and Kovács's Question on Cohomology of Fibers evidence for this event

This event attributed to ChatGPT 5.5 Pro

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Kollár and Kovács's Question on Cohomology of Fibers — Mathematical Frontier Network