论文标题
用于矢量束的模量圆形曲线的弹射庞加莱和皮卡德捆绑包在节点曲线
Projective Poincaré and Picard bundles for moduli spaces of vector bundles over nodal curves
论文作者
论文摘要
令$ u^{'s} _l（n，d）$为稳定的矢量捆绑包$ n $的模量空间，而确定$ l $其中$ l $是nodal曲线$ y $ y $ y $ y $ d $的固定线捆绑。我们证明，$ y \ y \ times u^{'s} _l（n，d）$和$ u^{'s} _l（n，d）$上的投射poincare捆绑包是适合偏振的。对于y $中的非词点$ x \，我们表明将投影庞贝里束的限制限制到$ x \ times u^{'s} _l（n，d）$对于任何极化都是稳定的。我们证明，对于算术属$ g \ ge 3 $，对于$ g = n = 2，d $奇数，Moduli space $ u'_l（n，d）的Picard group（n，d）$ a $ n $的nemable vector bundles a $ n $ $ l $ l $ l a $ d $ d $ d $ d $ insomorphic to $ \ mathbb insomorphic to Mathbbbbbbbbbbbbbb insomorphic to Isomorphic。
Let $U^{'s}_L(n,d)$ 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 Poincare bundle on $Y \times U^{'s}_L(n,d)$ and the projective Picard bundle on $U^{'s}_L(n,d)$ are stable for suitable polarisation. For a nonsingular point $x \in Y$, we show that the restriction of the projective Poincare bundle to $x \times U^{'s}_L(n,d)$ 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 $U'_L(n,d)$ of semistable vector bundles of rank $n$ with determinant $L$ of degree $d$ is isomorphic to $\mathbb{Z}$.
