A bound on the number of curves of a given degree through a general point of a projective variety
| dc.creator | Hwang, Jun-Muk | |
| dc.date | 2004-07-18 | |
| dc.date.accessioned | 2026-07-07T05:10:26Z | |
| dc.date.available | 2026-07-07T05:10:26Z | |
| dc.description | Let $X$ be an irreducible projective variety of dimension $n$ in a projective space and let $x$ be a point of $X$. Denote by ${\rm Curves}_d(X,x)$ the space of curves of degree $d$ lying on $X$ and passing through $x$. We will show that the number of components of ${\rm Curves}_d(X,x)$ for any smooth point $x$ outside a subvariety of codimension $\geq 2$ is bounded by a number depending only on $n$ and $d$. An effective bound is given. A key ingredient of the proof is an argument from Ein-Küchle-Lazarsfeld's work on Seshadri numbers. | |
| dc.description | to appear in Compositio Math | |
| dc.identifier | https://arxiv.org/abs/math/0407311 | |
| dc.identifier | http://arxiv.org/abs/math/0407311 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71931 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14J40 | |
| dc.title | A bound on the number of curves of a given degree through a general point of a projective variety | |
| dc.type | text |