For a smooth projective variety X ⊂ ℙr embedded by the complete linear system, Property Np has been studied for a long time (, , ,  etc.). On the other hand, Castelnuovo-Mumford regularity conjecture and related problems have been focused for a projective variety which is not necessarily linearly normal (, , , ,  etc.). This paper aims to explain the influence of Property Np on higher normality and defining equations of a smooth variety embedded by a sub-linear system. Also we prove a claim about Property Np of surface scrolls which is a generalization of Green's work in  about Property Np for curves.
ASJC Scopus subject areas
- Applied Mathematics