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

Sijong Kwak; Euisung Park

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

Sijong Kwak·Euisung Park

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Abstract

For a smooth projective variety $X\subset ¶^r$ 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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BibTeX RIS

Sijong Kwak, Euisung Park. 2004-04-14. Some effects of property $N_p$ on the higher normality and defining equations of nonlinearly normal varieties. https://arxiv.org/abs/math/0401026

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