Non-negative polynomials on generalized elliptic curves
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917224321646592 |
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| author | Kummer, Mario Zalar, Aljaž |
| author_facet | Kummer, Mario Zalar, Aljaž |
| contents | We study the cone of non-negative polynomials on generalized elliptic curves. We show that the zero set of every extreme ray has dense real points. If a generalized elliptic curve is embedded via a complete linear system, then we show that the convex hull of its real points (taken inside any affine chart containing all real points) is a spectrahedron. On the way, we generalize a result by Geyer--Martens on 2-torsion points in the Picard group of smooth real curves (of arbitrary genus) to possibly singular and reducible ones. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_13850 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-negative polynomials on generalized elliptic curves Kummer, Mario Zalar, Aljaž Functional Analysis Algebraic Geometry Classical Analysis and ODEs Primary 14P05, 14H52, Secondary 52A20 We study the cone of non-negative polynomials on generalized elliptic curves. We show that the zero set of every extreme ray has dense real points. If a generalized elliptic curve is embedded via a complete linear system, then we show that the convex hull of its real points (taken inside any affine chart containing all real points) is a spectrahedron. On the way, we generalize a result by Geyer--Martens on 2-torsion points in the Picard group of smooth real curves (of arbitrary genus) to possibly singular and reducible ones. |
| title | Non-negative polynomials on generalized elliptic curves |
| topic | Functional Analysis Algebraic Geometry Classical Analysis and ODEs Primary 14P05, 14H52, Secondary 52A20 |
| url | https://arxiv.org/abs/2508.13850 |