First Stiefel-Whitney class of real moduli spaces of stable maps to a convex surface
Abstract
Description
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 real structures induced by $c_X$ and any order two element $τ$ of permutation group $S_k$ acting on marked points. Each corresponding real part $\R_τ\bar{\mathcal{M}}_{0,k}(X,d)$ is a real normal projective variety. As the singular locus is of codimension bigger than two, these spaces thus carry a first 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 a homological description of these classes in term of the real part of boundary divisors of the space of stable maps.
33 pages, 10 figures, in French
33 pages, 10 figures, in French