Resumen de Some moduli stacks of symplectic bundles on a curve are rational

Indranil Biswas , Norbert Hoffmann

• Let C be a smooth projective curve of genus g2 over a field k. Given a line bundle L on C, let be the moduli stack of vector bundles E of rank 2n on C endowed with a nowhere degenerate symplectic form up to scalars. We prove that this stack is birational to for some s if deg(E)=ndeg(L) is odd and C admits a rational point PC(k) as well as a line bundle ? of degree 0 with . It follows that the corresponding coarse moduli scheme of Ramanathan-stable symplectic bundles is rational in this case.