On the first Stiefel-Whitney class of moduli space for real rational stable curves in the projective space

TL;DR

This paper computes the first Stiefel-Whitney class of the real moduli space of genus zero stable maps to projective three-space, using boundary divisors, when the evaluation map is generically finite.

Contribution

It provides a explicit representative for the first Stiefel-Whitney class of the real moduli space of rational curves in projective space, expanding understanding of its topological invariants.

Findings

Explicit representative for the first Stiefel-Whitney class derived.

Uses Poincaré duals of boundary divisors for computation.

Applicable when the evaluation map is generically finite.

Abstract

Moduli space of genus zero stable maps to the projective three-space naturally carries a real structure such that the fixed locus is a moduli space for real rational spatial curves with real marked points. The latter is a normal projective real variety. The singular locus being in codimension at least two, a first Stiefel-Whitney class is well defined. In this paper, we determine a representative for the first Stiefel-Whitney class of such real space when the evaluation map is generically finite. This can be done by means of Poincar\'e duals of boundary divisors.