A note on elliptic curves on toric surfaces

Fuente: arXiv
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Main Authors: Barash, Michael M., Tyomkin, Ilya
Format: Preprint
Published: 2025
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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