Noncomplete embeddings of rational surfaces
| dc.creator | Park, Euisung | |
| dc.date | 2004-10-13 | |
| dc.date.accessioned | 2026-07-07T05:13:14Z | |
| dc.date.available | 2026-07-07T05:13:14Z | |
| dc.description | In this paper, we study the Castelnuovo-Mumford regularity of nonlinearly normal embedding of rational surfaces. Let $X$ be a rational surface and let $L \in {Pic}X$ be a very ample line bundle. For a very ample subsystem $V \subset H^0 (X,L)$ of codimension $t \geq 1$, if $X \hookrightarrow ¶(V)$ satisfies Property $N^S_1$, then ${Reg} (X) \leq t+2$\cite{KP}. Thus we investigate Property $N^S_1$ of noncomplete linear systems on X. And our main result is about a condition of the position of $V$ in $H^0 (X,L)$ such that $X \hookrightarrow ¶(V)$ satisfies Property $N^S_1$. Indeed it is related to the geometry of a smooth rational curve of $X$. Also we apply our result to $¶^2$ and Hirzebruch surfaces. | |
| dc.description | 8 pages | |
| dc.identifier | https://arxiv.org/abs/math/0410309 | |
| dc.identifier | http://arxiv.org/abs/math/0410309 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72874 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Commutative Algebra | |
| dc.subject | 14N05; 14J26; 16E05 | |
| dc.title | Noncomplete embeddings of rational surfaces | |
| dc.type | text |