Desmic quartic surfaces in arbitrary characteristic
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909655384457216 |
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| author | Dolgachev, Igor Kondo, Shigeyuki |
| author_facet | Dolgachev, Igor Kondo, Shigeyuki |
| contents | A desmic quartic surface is a birational model of the Kummer surface of the self-product of an elliptic curve. We recall the classical geometry of these surfaces and study their analogs in arbitrary characteristic. Moreover, we discuss the cubic line complex $\frakG$ associated with the desmic tetrahedra introduced by G. Humbert. We prove that $\frakG$ is a rational $\bbQ$-Fano threefold with 34 nodes and the group of projective automorphisms isomorphic to $(\frakS_4\times \frakS_4)\rtimes 2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_01033 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Desmic quartic surfaces in arbitrary characteristic Dolgachev, Igor Kondo, Shigeyuki Algebraic Geometry A desmic quartic surface is a birational model of the Kummer surface of the self-product of an elliptic curve. We recall the classical geometry of these surfaces and study their analogs in arbitrary characteristic. Moreover, we discuss the cubic line complex $\frakG$ associated with the desmic tetrahedra introduced by G. Humbert. We prove that $\frakG$ is a rational $\bbQ$-Fano threefold with 34 nodes and the group of projective automorphisms isomorphic to $(\frakS_4\times \frakS_4)\rtimes 2$. |
| title | Desmic quartic surfaces in arbitrary characteristic |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2505.01033 |