Kollár and Kovács's Question on Cohomology of Fibers
Statement
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.
Context
A question of Kollár and Kovács on how badly cohomology can jump in flat families with good fibers.
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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.
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