Stability of the Poincaré bundle

Abstract

Let $C$ be a nonsingular projective curve of genus $g\ge 2$ defined over the complex numbers, and let $M_{\xi }$ denote the moduli space of stable bundles of rank $n$ and determinant $\xi$ on $C$, where $\xi$ is a line bundle of degree $d$ on $C$ and $n$ and $d$ are coprime. It is shown that the universal bundle $\cu_ξ$ on $C\times M_{\xi }$ is stable with respect to any polarisation on $C\times M_{\xi }$. It is shown further that the connected component of the moduli space of $\cu_ξ$ containing $\cu_ξ$ is isomorphic to the Jacobian of $C$.

16pp. Hard copy available from Dr. P. E. Newstead, Dept. of Pure Maths., University of Liverpool, Liverpool, L69 3BX, England. LaTeX 2.09

Cited by in corpus (6)

• On Picard bundles over Prym varieties
• On Chow Stability for algebraic curves
• Poincaré bundle for the fixed determinant moduli space on a nodal curve
• Deformations of the Picard Bundle
• Restriction of the Poincaré bundle to a Calabi-Yau hypersurface
• Universal Einstein-Hermitian Metrics