Prime Fano threefolds of genus 8 in positive characteristic
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915929680510976 |
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| author | Kanemitsu, Akihiro Tanaka, Hiromu |
| author_facet | Kanemitsu, Akihiro Tanaka, Hiromu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_08817 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Prime Fano threefolds of genus 8 in positive characteristic Kanemitsu, Akihiro Tanaka, Hiromu Algebraic Geometry 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. |
| title | Prime Fano threefolds of genus 8 in positive characteristic |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2604.08817 |