A refinement of Stein factorization and deformations of surjective morphisms
Abstract
This paper is concerned with a refinement of the Stein factorization, and with applications to the study of deformations of surjective morphisms. We show that every surjective morphism f:X->Y between normal projective varieties factors canonically via a finite cover of Y that is etale in codimension one. This "maximally etale factorization" is characterized in terms of positivity of the push-forward of the structure sheaf and satisfies a functorial property. It turns out that the maximally etale factorization is stable under deformations, and naturally decomposes an etale cover of the Hom-scheme into a torus and into deformations that are relative with respect to the rationally connected quotient of the target Y. In particular, we show that all deformations of f respect the rationally connected quotient of Y.
Cite
@article{arxiv.math/0508285,
title = {A refinement of Stein factorization and deformations of surjective morphisms},
author = {Stefan Kebekus and Thomas Peternell},
journal= {arXiv preprint arXiv:math/0508285},
year = {2007}
}