Cylinders in Fano threefolds of genus 9 and 10

Nikita Virin

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arXiv · 2605.30875

Cylinders in Fano threefolds of genus 9 and 10

Nikita Virin

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Abstract

We prove that any Fano threefold of genus 9 and 10 contains a cylinder, i.e. an open subset isomorphic to the product of a quasiprojective variety and the affine line. Moreover, we show that any Fano threefold of genus 10 has a point such that the Hilbert scheme of lines through the point has length three.

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Nikita Virin. 2026-05-29. Cylinders in Fano threefolds of genus 9 and 10. https://arxiv.org/abs/2605.30875

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