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

Ilia Nekrasov; Gaiane Panina; Alena Zhukova

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arXiv · 1707.04144

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

Ilia Nekrasov·Gaiane Panina·Alena Zhukova

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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.

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Ilia Nekrasov, Gaiane Panina, Alena Zhukova. 2017-07-13. Intersection numbers of Chern classes of tautological line bundles on the moduli spaces of flexible polygons. https://arxiv.org/abs/1707.04144

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