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Kollár and Kovács's Question on Cohomology of Fibers

Geometry & topology · posed by János Kollár, Sándor Kovács · disproved

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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.

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  1. construction · #1

    ChatGPT 5.5 Pro and Rethlas, with Jihao Liu

    The record says a model found this and names the people who worked on it. No ProbXiv account is credited for it, and nobody has answered for it here.

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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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