A Batyrev type classification of $Q$--factorial projective toric varieties

TL;DR

This paper extends Batyrev's classification of smooth complete toric varieties to the singular $Q$-factorial case and revises Kleinschmidt's classification of smooth complete toric varieties with Picard number 2.

Contribution

It generalizes Batyrev's classification to singular $Q$-factorial projective toric varieties and revises Kleinschmidt's classification for Picard number 2.

Findings

Extended classification to $Q$-factorial singular cases

Revised Kleinschmidt's classification for Picard number 2

Provided a comprehensive framework for classifying toric varieties

Abstract

The present paper is devoted to generalizing, inside the class of projective toric varieties, the classification [Batyrev91], performed by Batyrev in 1991 for smooth complete toric varieties, to the singular $Q$--factorial case. Moreover, in the first part of the paper the Kleinschmidt classification of smooth complete toric varieties of Picard number 2 [Kleinschmidt] is revised.