Enumeration of geometric Weierstrass points of metric graphs
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908425501278208 |
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| author | Bargans, Diego A. Robayo |
| author_facet | Bargans, Diego A. Robayo |
| contents | A classical result states that on a smooth algebraic curve of genus $g$ the number of Weierstrass points, counted with multiplicity, is $g^3-g$. In this paper, we introduce the notion of geometric Weierstrass points of metric graphs and show that a generic metric graph of genus $g$ has $g^3-g$ geometric Weierstrass points counted with multiplicity. Our methods also provide a new proof of the existence of Weierstrass points on metric graphs of genus bigger than or equal to $2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_22130 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Enumeration of geometric Weierstrass points of metric graphs Bargans, Diego A. Robayo Combinatorics Algebraic Geometry 14T15, 14T20 A classical result states that on a smooth algebraic curve of genus $g$ the number of Weierstrass points, counted with multiplicity, is $g^3-g$. In this paper, we introduce the notion of geometric Weierstrass points of metric graphs and show that a generic metric graph of genus $g$ has $g^3-g$ geometric Weierstrass points counted with multiplicity. Our methods also provide a new proof of the existence of Weierstrass points on metric graphs of genus bigger than or equal to $2$. |
| title | Enumeration of geometric Weierstrass points of metric graphs |
| topic | Combinatorics Algebraic Geometry 14T15, 14T20 |
| url | https://arxiv.org/abs/2506.22130 |