The degree of the divisor of jumping rational curves

dc.creatorRan, Ziv
dc.date2000-02-13
dc.date2000-03-16
dc.date.accessioned2026-07-07T04:33:50Z
dc.date.available2026-07-07T04:33:50Z
dc.descriptionFor 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.description16 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.identifierhttps://arxiv.org/abs/math/0002101
dc.identifierhttp://arxiv.org/abs/math/0002101
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58678
dc.subjectAlgebraic Geometry
dc.subject14n10, 14f05
dc.titleThe degree of the divisor of jumping rational curves
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