Intersection numbers of Chern classes of tautological line bundles on the moduli spaces of flexible polygons

Abstract

Given a flexible $n$-gon with generic side lengths, the moduli space of its configurations in ${\mathbb{R}}^2$ as well as in ${\mathbb{R}}^3$ is a smooth manifold. It is equipped with $n$ \textit{tautological} line bundles whose definition is motivated by M. Kontsevich's tautological bundles over ${\mathcal{M}}_{0,n}$. We study their Euler classes, first Chern classes and intersection numbers, that is, top monomials in Chern (Euler) classes. The latter are interpreted geometrically as the signed numbers of some \textit{triangular configurations} of the flexible polygon.