Fano Schemes of Lines on Toric Surfaces

TL;DR

This paper provides a complete description of the Fano scheme of lines on a projective toric surface, linking it directly to the geometry of the associated lattice polygon.

Contribution

It offers a novel, explicit characterization of the Fano scheme of lines for toric surfaces based on lattice polygon geometry.

Findings

Explicit description of the Fano scheme in terms of lattice polygons

Connection between toric surface geometry and Fano scheme structure

Complete classification for all projective toric surfaces

Abstract

We completely describe the Fano scheme of lines for a projective toric surface in terms of the geometry of the corresponding lattice polygon.