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arXiv · 2604.08817

Prime Fano threefolds of genus 8 in positive characteristic

Akihiro Kanemitsu·Hiromu Tanaka
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Abstract

We prove that a prime Fano threefold of genus 8 over an algebraically closed field of positive characteristic is isomorphic to a linear section of the Grassmannian variety Gr(2, 6). As applications, it is shown that a prime Fano threefold of genus 8 is irrational and, if the characteristic is larger than two, then it is globally F-regular.

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Akihiro Kanemitsu, Hiromu Tanaka. 2026-04-09. Prime Fano threefolds of genus 8 in positive characteristic. https://arxiv.org/abs/2604.08817

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