Courbe des trisécantes à une courbe elliptique lisse de \({\mathbb{P}}^ 3\). (The trisecant curve to a smooth elliptic curve of \({\mathbb{P}}^ 3.\)) (Q757515)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Courbe des trisécantes à une courbe elliptique lisse de \({\mathbb{P}}^ 3\). (The trisecant curve to a smooth elliptic curve of \({\mathbb{P}}^ 3.\)) |
scientific article; zbMATH DE number 4191876
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Courbe des trisécantes à une courbe elliptique lisse de \({\mathbb{P}}^ 3\). (The trisecant curve to a smooth elliptic curve of \({\mathbb{P}}^ 3.\)) |
scientific article; zbMATH DE number 4191876 |
Statements
Courbe des trisécantes à une courbe elliptique lisse de \({\mathbb{P}}^ 3\). (The trisecant curve to a smooth elliptic curve of \({\mathbb{P}}^ 3.\)) (English)
0 references
1991
0 references
Let C be a smooth elliptic curve in \({\mathbb{P}}^ 3\) of degree \( d\geq 5.\) It is shown that the trisecant curve T to C (embedded in the variety \(C_ 3\) of divisors of degree 3 on C) is connected [in fact \(h^ 0({\mathcal O}_ T)=1]\). The primary decomposition of T is studied in some detail when \(d=6\).
0 references
trisecant curve
0 references
