Noncommutative geometry of elliptic surfaces
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866910424863080448 |
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| author | Nikolaev, Igor |
| author_facet | Nikolaev, Igor |
| contents | We recast elliptic surfaces over the projective line in terms of the non-commutative tori and one-parameter families of the periodic continued fractions. The correspondence is used to study the Picard numbers, the ranks and the minimal models of such surfaces. As an example, we calculate the Picard numbers of elliptic surfaces with fibers having complex multiplication. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2106_11392 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Noncommutative geometry of elliptic surfaces Nikolaev, Igor Algebraic Geometry Number Theory Operator Algebras 11G05, 46L85 We recast elliptic surfaces over the projective line in terms of the non-commutative tori and one-parameter families of the periodic continued fractions. The correspondence is used to study the Picard numbers, the ranks and the minimal models of such surfaces. As an example, we calculate the Picard numbers of elliptic surfaces with fibers having complex multiplication. |
| title | Noncommutative geometry of elliptic surfaces |
| topic | Algebraic Geometry Number Theory Operator Algebras 11G05, 46L85 |
| url | https://arxiv.org/abs/2106.11392 |