A note on elliptic curves on toric surfaces

Abstract

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.

arXiv commentAccepted for publication in the Proceedings of the AMS

References in corpus (3)

• Monodromy of rational curves on toric surfaces
• Nonemptiness of Severi varieties on Enriques surfaces
• A note on the Severi problem for toric surfaces