On syzygies of projective varieties
type: Item
instance of: scholarly article
title: On syzygies of projective varieties
zbMATH Open document ID: 0898.14015
author: S. P. Inamdar
published in: Pacific Journal of Mathematics
publication date: 1997-10-08T00:00:00Z
review text: Let \(X\) be a projective variety over an algebraically closed field of characteristic zero. A line bundle \({\mathcal L}\) on \(X\) is said to have property \(N_p\) for some \(p>0\), if the ideal defining the embedding of \(X\) in the complete linear system of \({\mathcal L}\) is quadratically generated and has linear syzygies up to the \(p\)-th step. The author proves that for ample \({\mathcal L}\) and any \(p>0\), a sufficiently high power \({\mathcal L}^n\) has property \(N_p\), thereby generalizing the analogous result by \textit{L. Ein} and \textit{R. Lazarsfeld} in the smooth case [cf. Invent. Math. 111, No. 1, 51-67 (1993; Zbl 0814.14040)]. He expresses the hope that the explicit nature of the vanishing conditions used in his proof will lead to effective bounds for the required size of \(n\).
Mathematics Subject Classification ID: 14M05
Mathematics Subject Classification ID: 13D02
Mathematics Subject Classification ID: 14N05
Mathematics Subject Classification ID: 14C20
Mathematics Subject Classification ID: 14F05
zbMATH DE Number: 1054232
zbMATH Keywords: line bundle
zbMATH Keywords: embedding
zbMATH Keywords: syzygies
reviewed by: Martin Kreuzer
MaRDI profile type: Publication
full work available at URL: pjm.1997.177.71
OpenAlex ID: W2109444398
DOI: 10.2140/PJM.1997.177.71
description: scientific article; zbMATH DE number 1054232