English

A tree expansion formula of a homology intersection numbers on the configuration space $\mathcal{M}_{0,n}$

Combinatorics 2021-08-04 v1 High Energy Physics - Theory Mathematical Physics Algebraic Geometry math.MP

Abstract

In \cite{M}, Sebastian Mizera discovered a tree expansion formula of a homology intersection number on the configuration space M0,n\mathcal{M}_{0,n}. The formula originates in a study of Kawai-Lewellen-Tye relation in string theory. In this paper, we give an elementary proof of the formula. The basic ingredients are the combinatorics of the real moduli space M0,n(R)\overline{\mathcal{M}}_{0,n}(\R) and a combinatorial identity related to the face number of the associahedron.

Keywords

Cite

@article{arxiv.2010.14142,
  title  = {A tree expansion formula of a homology intersection numbers on the configuration space $\mathcal{M}_{0,n}$},
  author = {Saiei-Jaeyeong Matsubara-Heo},
  journal= {arXiv preprint arXiv:2010.14142},
  year   = {2021}
}

Comments

17 pages, 6 figures. Comments are welcome