Terminal toric Fano three-folds with certain numerical conditions

TL;DR

This paper classifies specific three-dimensional toric Fano varieties with terminal singularities, focusing on those where the sum of squared torus-invariant prime divisors is non-negative, providing a complete characterization.

Contribution

It offers a complete classification of Q-factorial terminal toric Fano three-folds under a particular numerical condition, advancing understanding in toric geometry.

Findings

Classification of all such three-folds achieved

Identification of conditions for non-negativity of divisor sums

Enhanced understanding of the structure of terminal toric Fano varieties

Abstract

We completely classify the Q-factorial terminal toric Fano three-folds such that the sum of the squared torus invariant prime divisors is non-negative.