Some moduli stacks of symplectic bundles on a curve are rational

Biswas, Indranil ; Hoffmann, Norbert (2008) Some moduli stacks of symplectic bundles on a curve are rational Advances in Mathematics, 219 (4). pp. 1150-1176. ISSN 0001-8708

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Official URL: http://linkinghub.elsevier.com/retrieve/pii/S00018...

Related URL: http://dx.doi.org/10.1016/j.aim.2008.06.001

Abstract

Let 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 ζ of degree 0 with ζ ⊗2 ≅ OC. It follows that the corresponding coarse moduli scheme of Ramanathan-stable symplectic bundles is rational in this case.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Symplectic Bundle; Moduli Stack; Rationality
ID Code:3582
Deposited On:12 Oct 2010 04:32
Last Modified:12 Oct 2010 04:32

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