On higher syzygies of ruled surfaces
| dc.creator | Park, Euisung | |
| dc.date | 2004-01-10 | |
| dc.date | 2004-09-22 | |
| dc.date.accessioned | 2026-07-07T05:04:28Z | |
| dc.date.available | 2026-07-07T05:04:28Z | |
| dc.description | We study higher syzygies of a ruled surface $X$ over a curve of genus $g$ with the numerical invariant $e$. Let $L \in {Pic}X$ be a line bundle in the numerical class of $aC_0 +bf$. We prove that for $0 \leq e \leq g-3$, $L$ satisfies property $N_p$ if $a \geq p+2$ and $b-ae \geq 3g-1-e+p$ and for $e \geq g-2$, $L$ satisfies property $N_p$ if $a \geq p+2$ and $b-ae\geq 2g+1+p$. By using these facts, we obtain Mukai type results. For ample line bundles $A_i$, we show that $K_X + A_1 + ... + A_q$ satisfies property $N_p$ when $0 \leq e < \frac{g-3}{2}$ and $q \geq g-2e+1 +p$ or when $e \geq \frac{g-3}{2}$ and $q \geq p+4$. Therefore we prove Mukai's conjecture for ruled surface with $e \geq \frac{g-3}{2}$. Also we prove that when $X$ is an elliptic ruled surface with $e \geq 0$, $L$ satisfies property $N_p$ if and only if $a \geq 1$ and $b-ae\geq 3+p$. | |
| dc.description | 19 pages, 3 figures | |
| dc.identifier | https://arxiv.org/abs/math/0401100 | |
| dc.identifier | http://arxiv.org/abs/math/0401100 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69814 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14J26 ; 16E05 | |
| dc.title | On higher syzygies of ruled surfaces | |
| dc.type | text |