Some examples in toric geometry

TL;DR

This paper explores specific examples in toric geometry, examining conditions under which quasitoric manifolds derived from certain polytopes and characteristic maps are almost complex.

Contribution

It provides new examples and criteria linking toric and quasitoric manifolds, focusing on almost complex structures.

Findings

Identifies conditions for quasitoric manifolds to be almost complex

Provides specific examples illustrating these conditions

Enhances understanding of the relationship between polytopes and manifold structures

Abstract

We present two examples in toric geometry concerning the relationship between toric and quasitoric manifolds, and provide the sufficient conditions on the base polytope and characteristic map so that the resulting quasitoric manifold is almost complex.