A note on elliptic curves on toric surfaces
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910249087139840 |
|---|---|
| author | Barash, Michael M. Tyomkin, Ilya |
| author_facet | Barash, Michael M. Tyomkin, Ilya |
| contents | In this paper, we study the Severi varieties parametrizing integral curves of geometric genus one on polarized toric surfaces in characteristic zero and describe their irreducible components. We show that the irreducible components are in natural bijection with certain affine sublattices of the lattice of characters of the toric surface. The sublattices are described explicitly in terms of the polygon defining the polarization of the toric surface. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_16966 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on elliptic curves on toric surfaces Barash, Michael M. Tyomkin, Ilya Algebraic Geometry 14H10, 14H52 In this paper, we study the Severi varieties parametrizing integral curves of geometric genus one on polarized toric surfaces in characteristic zero and describe their irreducible components. We show that the irreducible components are in natural bijection with certain affine sublattices of the lattice of characters of the toric surface. The sublattices are described explicitly in terms of the polygon defining the polarization of the toric surface. |
| title | A note on elliptic curves on toric surfaces |
| topic | Algebraic Geometry 14H10, 14H52 |
| url | https://arxiv.org/abs/2503.16966 |