dc.contributor.author | Hitching, George H. | en_US |
dc.date.accessioned | 2014-03-19T09:36:47Z | |
dc.date.available | 2014-03-19T09:36:47Z | |
dc.date.issued | 2013 | en_US |
dc.identifier.citation | Hitching, G. (2013). Geometry of Vector Bundle Extensions and Applications to a Generalised Theta Divisor. Mathematica Scandinavica, 112(1) | en_US |
dc.identifier.issn | 0025-5521 | en_US |
dc.identifier.other | FRIDAID 1040325 | en_US |
dc.identifier.uri | https://hdl.handle.net/10642/1910 | |
dc.description.abstract | Let E and F be vector bundles over a complex projective smooth curve X, and suppose that 0→E→W→F→0 is a nontrivial extension. Let G⊆F be a subbundle and D an effective divisor on X. We give a criterion for the subsheaf G(−D)⊂F to lift to W, in terms of the geometry of a scroll in the extension space PH1(X,Hom(F,E)). We use this criterion to describe the tangent cone to the generalised theta divisor on the moduli space of semistable bundles of rank r and slope g−1 over X, at a stable point. This gives a generalisation of a case of the Riemann-Kempf singularity theorem for line bundles over X. In the same vein, we generalise the geometric Riemann-Roch theorem to vector bundles of slope g−1 and arbitrary rank. | en_US |
dc.language.iso | eng | en_US |
dc.publisher | Mathematica Scandinavica | en_US |
dc.relation.ispartofseries | Mathematica Scandinavica;112(1) | en_US |
dc.subject | Vector bundle extensions | en_US |
dc.title | Geometry of Vector Bundle Extensions and Applications to a Generalised Theta Divisor | en_US |
dc.type | Journal article | en_US |
dc.type | Peer reviewed | en_US |
dc.identifier.doi | http://www.mscand.dk/article/view/15233 | |