Rationality and Poincare families for vector bundles with extra structure on a curve

Details Rationality and Poincare families for vector bundles with extra structure on a curve Rationality and Poincare families for vector bundles with extra structure on a curve

2005-11-27

arxiv.org/abs/math/0511656v1

Int. Math. Res. Not. (Vol. 2007), article ID rnm010 (29 pages)

Mathematics

Algebraic Geometry

19 pages AMSLaTeX

Scientific paper

Iterated 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 Poincare families on finite coverings of the moduli schemes.

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