Building planar polygon spaces from the projective braid arrangement

Author:

Daundkar Navnath1,Deshpande Priyavrat2ORCID

Affiliation:

1. Department of Mathematics , Indian Institute of Science Education and Research , Pune , India

2. Department of Mathematics , 232555 Chennai Mathematical Institute , Chennai , India

Abstract

Abstract The moduli space of planar polygons with generic side lengths is a smooth, closed manifold. It is known that these manifolds contain the moduli space of distinct points on the real projective line as an open dense subset. Kapranov showed that the real points of the Deligne–Mumford–Knudson compactification can be obtained from the projective Coxeter complex of type 𝐴 (equivalently, the projective braid arrangement) by iteratively blowing up along the minimal building set. In this paper, we show that these planar polygon spaces can also be obtained from the projective Coxeter complex of type 𝐴 by performing an iterative cellular surgery along a subcollection of the minimal building set. Interestingly, this subcollection is determined by the combinatorial data associated with the length vector called the genetic code.

Funder

Science and Engineering Research Board

Publisher

Walter de Gruyter GmbH

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