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Let $(X,c_X)$ be a convex projective surface equipped with a real structure.The space of stable maps $\bar{\mathcal{M}}_{0,k}(X,d)$ carries different realstructures induced by $c_X$ and any order two element $\tau$ of permutationgroup $S_k$ acting on marked points. Each corresponding real part$\R_{\tau}\bar{\mathcal{M}}_{0,k}(X,d)$ is a real normal projective variety. Asthe singular locus is of codimension bigger than two, these spaces thus carry afirst Stiefel-Whitney class for which we determine a representative in the case$k=c_1(X)d-1$ where $c_1(X)$ is the first Chern class of $X$. Namely, we give ahomological description of these classes in term of the real part of boundarydivisors of the space of stable maps.

First Stiefel-Whitney class of real moduli spaces of stable maps to a convex surface