Arthur Renaudineau, Université de Lille
Oleg Viro’s combinatorial patchworking is one of the most powerful tool to construct real algebraic varieties with controlled topology. In a joint work in progress with Diego Matessi, we explore combinatorial patchworking in the case of reflexive polytopes. It appears that they are parametrized by mod 2 divisor classes in the mirror variety (obtained by considering the dual polytope). I will present some results and conjectures which relate the homology of the real part to the cup product of divisor classes in the mirror.