2013-06-272013-06-272008Biswas, I. & Hoffmann, N. (2008), 'Some moduli stacks of symplectic bundles on a curve are rational ', Advances in Mathematics, Vol. 219(4), p 1150-1176.http://hdl.handle.net/10395/1975Let C be a smooth projective curve of genus g ≥ 2 over a field k. Given a line bundle L on C, let Sympl2n,L be the moduli stack of vector bundles E of rank 2n on C endowed with a nowhere degenerate symplectic form b : E ⊗ E −→ L up to scalars. We prove that this stack is birational to BGm × As for some s if deg(E) = n · deg(L) is odd and C admits a rational point P ∈ C(k) as well as a line bundle ξ of degree 0 with ξ⊗2 􀀀∼= OC . It follows that the corresponding coarse moduli scheme of Ramanathan-stable symplectic bundles is rational in this case.eng© Elsevier, The original publication of Biswas, I. & Hoffmann, N. (2008), 'Some moduli stacks of symplectic bundles on a curve are rational ', Advances in Mathematics, Vol. 219(4), p 1150-1176 is available at http://dx.doi.org/10.1016/j.aim.2008.06.001Moduli stackSymplectic bundlesArticlehttp://dx.doi.org/10.1016/j.aim.2008.06.001