Let $U_L^{\prime s}(n,d)$ be the moduli space of stable vector bundles of rank n with determinant L where L is a fixed line bundle of degree d over a nodal curve Y. We prove that the projective Poincaré bundle on $Y\times U_L^{\prime s}(n,d)$ and the projective Picard bundle on $U_L^{\prime s}(n,d)$ are stable for suitable polarisations. For a nonsingular point $x\in Y$, we show that the restriction of the projective Poincaré bundle to $\{x\}\times U_L^{\prime s}(n,d)$ is stable for any polarisation. We prove that for arithmetic genus $g\ge 3$ and for $g=n=2,d$ odd, the Picard group of the moduli space $U_L^{\prime }(n,d)$ of semistable vector bundles of rank n with determinant L of degree d is isomorphic to $\mathbb{Z}$.

让 ${ü}_{\mathrm{大号}}^{\prime s}（ñ，d）$是行列式为L的秩为n的稳定矢量束的模空间，其中L为节点曲线Y上度为d的固定线束。我们证明射影庞加莱束$ÿ\times {ü}_{\mathrm{大号}}^{\prime s}（ñ，d）$ 和投射的Picard束 ${ü}_{\mathrm{大号}}^{\prime s}（ñ，d）$对合适的极化稳定。对于非奇异点$X\in ÿ$，我们证明了射影庞加莱束对 $\{X\}\times {ü}_{\mathrm{大号}}^{\prime s}（ñ，d）$对任何极化稳定。我们证明对于算术属$G\ge 3$ 和为 $G=ñ=2，d$ 奇数，模空间的皮卡德群 ${ü}_{\mathrm{大号}}^{\prime }（ñ，d）$秩的半稳定矢量束Ñ与行列式大号度d是同构$\mathbb{ž}$。