Sur le morphisme de Barth
| dc.creator | Potier, Joseph Le | |
| dc.creator | Tikhomirov, Alexander | |
| dc.date | 2000-03-02 | |
| dc.date.accessioned | 2026-07-07T04:34:11Z | |
| dc.date.available | 2026-07-07T04:34:11Z | |
| dc.description | Let ${\rm F}$ be a rank-2 semi-stable sheaf on the projective plane, with Chern classes $c_{1}=0,c_{2}=n$. The curve $β_{\rm F}$ of jumping lines of ${\rm F}$, in the dual projective plane, has degree $n$. Let ${\rm M}_{n}$ be the moduli space of equivalence classes of semi-stables sheaves of rank 2 and Chern classes $(0,n)$ on the projective plane and ${\cal C}_{n}$ be the projective space of curves of degree $n$ in the dual projective plane. The Barth morphism $$β: {\rm M}_{n}\longrightarrow{\cal C}_{n}$$ associates the point $β_{\rm F}$ to the class of the sheaf ${\rm F}$. We prove that this morphism is generically injective for $n\geq 4.$ The image of $β$ is a closed subvariety of dimension $4n-3$ of ${\cal C}_{n}$; as a consequence of our result, the degree of this image is given by the Donaldson number of index $4n-3$ of the projective plane. | |
| dc.description | Plain.tex, 54 pages. Uses diagrams.tex | |
| dc.identifier | https://arxiv.org/abs/math/0003016 | |
| dc.identifier | http://arxiv.org/abs/math/0003016 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/58803 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14D20 | |
| dc.title | Sur le morphisme de Barth | |
| dc.type | text |