# Small covers over wedges of polygons

## TL;DR

This paper classifies small covers and real toric manifolds with orbit spaces derived from polygons through wedging, using combinatorial puzzles to systematically analyze their structure.

## Contribution

It introduces a systematic combinatorial method to classify small covers and real toric manifolds over wedge polygons, expanding understanding of their topological and combinatorial properties.

## Key findings

- Classification of small covers over wedge polygons
- Development of a combinatorial puzzle method
- Identification of new classes of real toric manifolds

## Abstract

A small cover is a closed smooth manifold of dimension $n$ having a locally standard $\mathbb{Z}_2^n$-action whose orbit space is isomorphic to a simple polytope. A typical example of small covers is a real projective toric manifold (or, simply, a real toric manifold), that is, a real locus of projective toric manifold. In the paper, we classify small covers and real toric manifolds whose orbit space is isomorphic to the dual of the simplicial complex obtainable by a sequence of wedgings from a polygon, using a systematic combinatorial method finding toric spaces called puzzles.