The numerical class of a surface on a toric manifold

TL;DR

This paper introduces a method to describe the numerical class of torus invariant surfaces on projective toric manifolds and applies it to classify certain toric 2-Fano manifolds.

Contribution

It provides a new approach to describe numerical classes of surfaces on toric manifolds and classifies specific toric 2-Fano manifolds based on this method.

Findings

Classified toric 2-Fano manifolds of Picard number 2

Classified toric 2-Fano manifolds of dimension at most 4

Developed a method to describe numerical classes of torus invariant surfaces

Abstract

In this paper, we give a method to describe the numerical class of a torus invariant surface on a projective toric manifold. As applications, we can classify toric 2-Fano manifolds of Picard number 2 or of dimension at most 4.