Some effects of Veronese map on syzygies of projective varieties
| dc.creator | Park, Euisung | |
| dc.date | 2005-09-30 | |
| dc.date | 2005-11-08 | |
| dc.date.accessioned | 2026-07-07T06:43:09Z | |
| dc.date.available | 2026-07-07T06:43:09Z | |
| dc.description | Let $X \subset ¶^r$ be a nondegenerate projective variety and let $ν_{\ell} : ¶^r \to ¶^N$ be the $\ell$-th Veronese embedding. In this paper we study the higher normality, defining equations and syzygies among them for the projective embedding $ν_{\ell} (X) \subset ¶^N$. We obtain that for a very ample line bundle $L \in {Pic}X$ such that $X \subset ¶H^0 (X,L)$ is $m$-regular in the sense of Castelnuovo-Mumford, $(X,L^{\ell})$ satisfies property $N_{\ell}$ for all $\ell \geq m$ (Theorem \ref{thm:main1}). This is a generalization of M. Green's work that $(¶^r,\mathcal{O}_{¶^r} (\ell))$ satisfies property $N_{\ell}$. Also our result refines works of Ein-Lazarsfeld in \cite{EL}, Gallego-Purnaprajna in \cite{GP} and E. Rubei in \cite{Rubei1}, \cite{Rubei} and \cite{Ru1}. | |
| dc.description | 16 pages | |
| dc.identifier | https://arxiv.org/abs/math/0509710 | |
| dc.identifier | http://arxiv.org/abs/math/0509710 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/102309 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 13D02; 14N15 | |
| dc.title | Some effects of Veronese map on syzygies of projective varieties | |
| dc.type | text |