Euler characteristic of the space of real multivariate irreducible polynomials

Abstract

We compute the compactly supported Euler characteristic of the space of degree $d$ irreducible polynomials in $n$ variables with real coefficients and show that the values are given by the digits in the so-called balanced binary expansion of the number of variables $n$.

11 pages, split and expanded from 1811.08601, comments welcome. arXiv admin note: text overlap with arXiv:1811.08601