On the gamma_2-positivity of Smooth Toric Threefolds

Abstract

In this thesis we consider the classification of smooth toric varieties with positive second chern character. We give a complete proof, without using the classification of smooth toric Fano threefolds, that the only such threefold with positive second chern character is $\mathbb{P}^3$. We also provide some initial steps towards proving that the only smooth toric Fano varieties in any dimension with positive second chern character are the projective spaces $\mathbb{P}^n$.