Some Moduli Stacks of Symplectic Bundles on a Curve Are Rational

@inproceedings{Biswas2006SomeMS,
  title={Some Moduli Stacks of Symplectic Bundles on a Curve Are Rational},
  author={Indranil Biswas and Norbert Hoffmann},
  year={2006}
}
Let C be a smooth projective curve of genus g ≥ 2 over a field k. Given a line bundle L on C, let Sympl 2n,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 × A s for some s if deg(E) = n · deg(L) is odd and C admits a… CONTINUE READING