Some moduli stacks of symplectic bundles on a curve are rational |
| |
Authors: | Indranil Biswas |
| |
Affiliation: | a School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India b Mathematisches Institut der Georg-August-Universität, Bunsenstraße 3-5, 37073 Göttingen, Germany |
| |
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 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 ξ of degree 0 with ξ⊗2?OC. It follows that the corresponding coarse moduli scheme of Ramanathan-stable symplectic bundles is rational in this case. |
| |
Keywords: | 14H60 14A20 |
本文献已被 ScienceDirect 等数据库收录! |
|