Monomial Transformations of the Projective Space
Résumé
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.
Domaines
Géométrie algébrique [math.AG]
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