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

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

2008-07-18

arxiv.org/abs/0807.3018v3

Mathematics

Algebraic Geometry

16 pages, 6 figures, in French

Scientific paper

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.

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