The distribution of Weierstrass points on a tropical curve
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2018
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909126130401280 |
|---|---|
| author | Richman, David Harry |
| author_facet | Richman, David Harry |
| contents | We show that on a metric graph of genus $g$, a divisor of degree $n$ generically has $g(n-g+1)$ Weierstrass points. For a sequence of generic divisors on a metric graph whose degrees grow to infinity, we show that the associated Weierstrass points become distributed according to the Zhang canonical measure. In other words, the limiting distribution is determined by effective resistances on the metric graph. This distribution result has an analogue for complex algebraic curves, due to Neeman, and for curves over non-Archimedean fields, due to Amini. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1809_07920 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | The distribution of Weierstrass points on a tropical curve Richman, David Harry Algebraic Geometry Combinatorics Metric Geometry 14T15 (Primary), 05C22, 14H55, 57M12, 60B10, 94C05 (Secondary) We show that on a metric graph of genus $g$, a divisor of degree $n$ generically has $g(n-g+1)$ Weierstrass points. For a sequence of generic divisors on a metric graph whose degrees grow to infinity, we show that the associated Weierstrass points become distributed according to the Zhang canonical measure. In other words, the limiting distribution is determined by effective resistances on the metric graph. This distribution result has an analogue for complex algebraic curves, due to Neeman, and for curves over non-Archimedean fields, due to Amini. |
| title | The distribution of Weierstrass points on a tropical curve |
| topic | Algebraic Geometry Combinatorics Metric Geometry 14T15 (Primary), 05C22, 14H55, 57M12, 60B10, 94C05 (Secondary) |
| url | https://arxiv.org/abs/1809.07920 |