Some effects of property Nₚ on the higher normality and defining equations of nonlinearly normal varieties

الأصل · EN

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