Computation of the first Stiefel-Whitney class for the variety $\overline{{\mathcal M}_{0,n}^{\mathbb R}}$

TL;DR

This paper calculates the first Stiefel-Whitney class for the real moduli space of genus 0 curves with marked points, using its natural cell decomposition to express the class explicitly.

Contribution

It provides an explicit computation of the first Stiefel-Whitney class for the real moduli space of genus 0 curves, linking topological invariants to cell decomposition.

Findings

Explicit formula for the first Stiefel-Whitney class

Connection between topological invariants and cell decomposition

Advancement in understanding real algebraic moduli spaces

Abstract

We compute the class which is Poincare dual to the first Stiefel-Whitney class for the Deligne-Mumford compactification of the moduli space of real algebraic curves of genus 0 with n marked and numbered points in terms of the natural cell decomposition of the variety under consideration.