On the moduli space of polygons with area center

Abstract

A point p is said to be an area center of a polygon if all of the triangles composed of p and its edges have one and the same area. We construct a moduli space ACn of such n-gons and study its geometry and arithmetic. For every n≥5, the moduli space is proved to be a rational complete intersection subvariety in An. With the help of some subvarieties of low degree in ACn, we also find a unified method of construction of good-looking polygons with area center.