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

Details Some effects of property $N_p$ on the higher normality and defining equations of nonlinearly normal varieties Some effects of property $N_p$ on the higher normality and defining equations of nonlinearly normal varieties

2004-01-05

arxiv.org/abs/math/0401026v2

Mathematics

Algebraic Geometry

18 pages, 2 tables

Scientific paper

For a smooth projective variety $X\subset \P^r$ embedded by the complete linear system, Property $N_p$ 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 $N_p$ on higher normality and defining equations of a smooth variety embedded by sub-linear system. Also we prove a claim about Property $N_p$ of surface scrolls which is a generalization of Green's work in \cite{Green} about Property $N_p$ for curves.

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