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| Format: | Preprint |
| Veröffentlicht: |
2023
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| Online-Zugang: | https://arxiv.org/abs/2304.09955 |
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| _version_ | 1866913551737683968 |
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| author | Kuznetsova, Alexandra |
| author_facet | Kuznetsova, Alexandra |
| contents | We study obstructions to rationality on a nodal Fano threefold $M$ that is a double cover of a smooth quadric threefold ramified over an intersection with a quartic threefold in $\mathbb{P}^4$. We prove that if $M$ admits an Artin--Mumford obstruction to rationality then it lies in one of three explicitly described families. Conversely, a general element of any of these families admits an Artin--Mumford obstruction to rationality. Only one of these three families was known before; other two families of nodal Fano threefolds with obstructions to rationality are new. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_09955 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Double covers of smooth quadric threefolds with Artin-Mumford obstructions to rationality Kuznetsova, Alexandra Algebraic Geometry We study obstructions to rationality on a nodal Fano threefold $M$ that is a double cover of a smooth quadric threefold ramified over an intersection with a quartic threefold in $\mathbb{P}^4$. We prove that if $M$ admits an Artin--Mumford obstruction to rationality then it lies in one of three explicitly described families. Conversely, a general element of any of these families admits an Artin--Mumford obstruction to rationality. Only one of these three families was known before; other two families of nodal Fano threefolds with obstructions to rationality are new. |
| title | Double covers of smooth quadric threefolds with Artin-Mumford obstructions to rationality |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2304.09955 |