Monomial transformations of the projective space

Abstract

We prove that, over any field, the dimension of the indeterminacy locus of a rational map f : Pn → Pn defined by monomials of the same degree d with no common factors is at least (n - 2)/2, provided that the degree of f as a map is not divisible by d. This implies upper bounds on the multidegree of f and in particular, when f is birational, on the degree of f−1.