Simplicial resolutions and spaces of algebraic maps between real projective spaces

Abstract

We show that the space A˜d(m,n) consisting of all real projective classes of (n+1)-tuples of real coefficients homogeneous polynomials of degree d in (m+1) variables, without common real roots except zero, has the same homology as the space Map(RPm,RPn) of continuous maps from the m-dimensional real projective space RPm into the n real dimensional projective space RPn up to dimension (n−m)(d+1)−1. This considerably improves the main result of Adamaszek et al. (2011) [1].