The degree of the divisor of jumping rational curves
| dc.creator | Ran, Ziv | |
| dc.date | 2000-02-13 | |
| dc.date | 2000-03-16 | |
| dc.date.accessioned | 2026-07-07T04:33:50Z | |
| dc.date.available | 2026-07-07T04:33:50Z | |
| dc.description | For a semistable reflexive sheaf $E$ of rank $r$ and $c_1=a$ on $¶^n$ and an integer $d$ such that $r|ad$, we give sufficient conditions so that the restriction of $E$ on a generic rational curve of degree $d$ is balanced, i.e. a twist of the trivial bundle (for instance, if $E$ has balanced restriction on a generic line, or $r=2$ or $E$ is an exterior power of the tangent bundle). Assuming this, we give a formula for the 'virtual degree', interpreted enumeratively, of the locus of rational curves of degree $d$ on which the restriction of $E$ is not balanced, generalizing a classical formula due to Barth for the degree of the divisor of jumping lines of a semistable rank-2 bundle. | |
| dc.description | 16 pages amstex. The revised version contains some further examples and applications, a more explicit mention of the connection with quantum K-theory, and a self-contained accout of the Chow compactification of the space of rational curves | |
| dc.identifier | https://arxiv.org/abs/math/0002101 | |
| dc.identifier | http://arxiv.org/abs/math/0002101 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/58678 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14n10, 14f05 | |
| dc.title | The degree of the divisor of jumping rational curves | |
| dc.type | text |