Totally invariant divisors of endomorphisms of projective spaces

Abstract

Totally invariant divisors of endomorphisms of the projective space are expected to be always unions of linear spaces. Using logarithmic differentials we establish a lower bound for the degree of the non-normal locus of a totally invariant divisor. As a consequence we prove the linearity of totally invariant divisors for ${\mathbb{P}}^3$.

arXiv comment9 pages, changed metadata