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Some moduli stacks of symplectic bundles on a curve are rational

Authors
Journal
Advances in Mathematics
0001-8708
Publisher
Elsevier
Publication Date
Volume
219
Issue
4
Identifiers
DOI: 10.1016/j.aim.2008.06.001
Keywords
  • Symplectic Bundle
  • Moduli Stack
  • Rationality

Abstract

Abstract Let C be a smooth projective curve of genus g ⩾ 2 over a field k. Given a line bundle L on C, let S ympl 2 n , L be the moduli stack of vector bundles E of rank 2 n on C endowed with a nowhere degenerate symplectic form b : E ⊗ E → L up to scalars. We prove that this stack is birational to B G m × A s 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 ≇ O C . It follows that the corresponding coarse moduli scheme of Ramanathan-stable symplectic bundles is rational in this case.

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