Reflexive polygons and rational elliptic surfaces

TL;DR

This paper explores the geometry of eight rational elliptic surfaces linked to reflexive polygons, revealing their connection to mirror symmetry and del Pezzo surfaces with very ample anticanonical bundles.

Contribution

It provides a detailed geometric analysis of these surfaces and their relation to mirror symmetry and del Pezzo surfaces, a novel connection in algebraic geometry.

Findings

Identification of eight rational elliptic surfaces associated with reflexive polygons

Establishment of mirror symmetry correspondence with del Pezzo surface families

Insights into the geometry of elliptic fibrations and their algebraic properties

Abstract

In this note we study in detail the geometry of eight rational elliptic surfaces naturally associated to the sixteen reflexive polygons. The elliptic fibrations supported by these surfaces correspond under mirror symmetry to the eight families of smooth del Pezzo surfaces with very ample anticanonical bundle.