Wedge operations and a new family of projective toric manifolds

TL;DR

This paper classifies toric manifolds over complexes derived from wedge operations on polygons, proving all such manifolds are projective and providing an infinite family of these manifolds.

Contribution

It offers a complete classification of toric manifolds over wedge-derived complexes and establishes their projectivity, introducing an infinite family of projective toric manifolds.

Findings

All toric manifolds over P_m(J) are projective.

Provides an explicit classification of these manifolds.

Introduces an infinite family of projective toric manifolds.

Abstract

Let $P_m(J)$ denote a simplicial complex obtainable from consecutive wedge operations from an $m$-gon. In this paper, we completely classify toric manifolds over $P_m(J)$ and prove that all of them are projective. As a consequence, we provide an infinite family of projective toric manifolds.