Distribution of the eigenvalues of a random system of homogeneous polynomials

Paul Breiding, Peter Bürgisser

Let $f=(f_1,\dots ,f_n)$ be a system of $n$ complex homogeneous polynomials in $n$ variables of degree $d$. We call $\lambda \in \mathbb{C}$ an eigenvalue of $f$ if there exists $v\in\math…