Some moduli stacks of symplectic bundles on a curve are rational
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Let C be a smooth projective curve of genus at least 2 over a field k. Given a line bundle L on C, we consider the moduli stack of rank 2n vector bundles E on C endowed with a nowhere degenerate symplectic form $b: E \otimes E \to L$ up to scalars. We prove that this stack is birational to BG_m times an affine space A^s if n and the degree of L are both odd and C admits a k-rational point as well as a line bundle of degree 0 whose square is nontrivial. It follows that the corresponding coarse moduli scheme is rational in this case.
18 pages. v2: minor changes, following the referee's suggestions. published version
18 pages. v2: minor changes, following the referee's suggestions. published version