Kummer surfaces and quadratic line complexes in characteristic two
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866911305410019328 |
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| author | Katsura, Toshiyuki Kondo, Shigeyuki |
| author_facet | Katsura, Toshiyuki Kondo, Shigeyuki |
| contents | In this paper, we study the classical theory of quadratic line complexes and Kummer surfaces. A quadratic line complex is the intersection of the Grassmannian $G(2,4)$ and a quadric hypersurface in ${\bf P}^5$, and a Kummer surface is the quotient of the Jacobian of a curve of genus 2 by the inversion. F. Klein discovered a relationship between a quadratic line complex and a curve of genus 2, its Jacobian and the associated Kummer surface. This theory holds in any characteristic not equal to two. However the situation in characteristic two is entirely different. The purpose of this paper is to give an analogue in characteristic 2 of this classical theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_01450 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Kummer surfaces and quadratic line complexes in characteristic two Katsura, Toshiyuki Kondo, Shigeyuki Algebraic Geometry 14J28 (Primary) 14G17 (Secondary) In this paper, we study the classical theory of quadratic line complexes and Kummer surfaces. A quadratic line complex is the intersection of the Grassmannian $G(2,4)$ and a quadric hypersurface in ${\bf P}^5$, and a Kummer surface is the quotient of the Jacobian of a curve of genus 2 by the inversion. F. Klein discovered a relationship between a quadratic line complex and a curve of genus 2, its Jacobian and the associated Kummer surface. This theory holds in any characteristic not equal to two. However the situation in characteristic two is entirely different. The purpose of this paper is to give an analogue in characteristic 2 of this classical theory. |
| title | Kummer surfaces and quadratic line complexes in characteristic two |
| topic | Algebraic Geometry 14J28 (Primary) 14G17 (Secondary) |
| url | https://arxiv.org/abs/2301.01450 |