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algebra / Algebraic geometry

Baker's Question on Smooth Hyperplane Sections over Finite Fields

Baker asked, as recorded by Poonen, whether a fixed smooth quasiprojective variety over a finite field must acquire a smooth rational hyperplane section after every sufficiently high-dimensional linearly nondegenerate embedding. Poonen predicted no for every positive-dimensional variety, and that prediction is correct.

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algebraJun 22, 2026Significance 15/100Registry: unreviewed

Baker's Question on Smooth Hyperplane Sections over Finite Fields

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Baker asked, as recorded by Poonen, whether a fixed smooth quasiprojective variety over a finite field must acquire a smooth rational hyperplane section after every sufficiently high-dimensional linearly nondegenerate embedding. Poonen predicted no for every positive-dimensional variety, and that prediction is correct.

Source authenticatedBaker's Question on Smooth Hyperplane Sections over Finite Fields →
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Baker asked, as recorded by Poonen, whether a fixed smooth quasiprojective variety over a finite field must acquire a smooth rational hyperplane section after every sufficiently high-dimensional linearly nondegenerate embedding. Poonen predicted no for every positive-dimensional variety, and that prediction is correct.

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