A refinement of Stein factorization and deformations of surjective morphisms
| dc.creator | Kebekus, Stefan | |
| dc.creator | Peternell, Thomas | |
| dc.date | 2005-08-16 | |
| dc.date.accessioned | 2026-07-07T05:22:24Z | |
| dc.date.available | 2026-07-07T05:22:24Z | |
| dc.description | 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. | |
| dc.identifier | https://arxiv.org/abs/math/0508285 | |
| dc.identifier | http://arxiv.org/abs/math/0508285 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76045 | |
| dc.subject | Algebraic Geometry | |
| dc.title | A refinement of Stein factorization and deformations of surjective morphisms | |
| dc.type | text |