2013-05-302013-05-302007Hoffmann, N. (2007), 'Rationality and Poincaré Families for Vector Bundles with Extra Structure on a Curve', International Mathematics Research Notices, Vol. 2007.http://dx.doi.org/10.1093/imrn/rnm010http://hdl.handle.net/10395/1918Iterated Grassmannian bundles over moduli stacks of vector bundles on a curve are shown to be birational to an affine space times a moduli stack of degree 0 vector bundles, following the method of King and Schofield. Applications include the birational type of some Brill-Noether loci, of moduli schemes for vector bundles with parabolic structure or with level structure and for A. Schmitt’s decorated vector bundles. A further consequence concerns the existence of Poincaré families on finite coverings of the moduli schemes.engThis is a pre-copy-editing, author-produced PDF of an article accepted for publication in (IMRN) International Mathematics Research Notices (2007) Vol. 2007 following peer review. The definitive publisher-authenticated version - Hoffman, N. (2007), 'Rationality and Poincaré Families for Vector Bundles with Extra Structure on a Curve', International Mathematics Research Notices, Vol. 2007 is available online at: http://dx.doi.org/10.1093/imrn/rnm010Vector bundlesPoincaré familiesCurveArticle