String Dualities and Toric Geometry: An Introduction

TL;DR

This paper introduces key concepts of toric geometry essential for understanding string and F-theory dualities, emphasizing intuitive explanations and precise rules for working with toric varieties.

Contribution

It provides an accessible introduction to toric geometry tailored for applications in string and F-theory dualities, focusing on homogeneous coordinates and weighted projective spaces.

Findings

Clarifies the definition of toric varieties via homogeneous coordinates

Provides intuitive and precise explanations of toric geometry concepts

Facilitates understanding of string and F-theory dualities through toric geometry

Abstract

This note is supposed to be an introduction to those concepts of toric geometry that are necessary to understand applications in the context of string and F-theory dualities. The presentation is based on the definition of a toric variety in terms of homogeneous coordinates, stressing the analogy with weighted projective spaces. We try to give both intuitive pictures and precise rules that should enable the reader to work with the concepts presented here.