论文标题
Brill - 在曲线上的符号束的模量空间上
Brill--Noether loci on moduli spaces of symplectic bundles over curves
论文作者
论文摘要
与曲线$ c $相关的符号brill - noether-locus $ {\ mathcal s} _ {2n，k}^k $与$ c $ coparties stable $ 2n $ c $相关的$ c $，至少$ k $ extions $ c $ bundles tity $ k $ extions，它们含有skewsymmetric birinear can can on nondementer skewsymmetric bul can canonor canonor canonorical bul canononical canonorical bul。这是一种对称的决定性品种，其切线空间由对称的培养皿图定义。我们在$ {\ Mathcal s} _ {2n，k}^k $的各个组件的尺寸上获得上限。我们显示了几个$ {\ Mathcal s} _ {2n，k}^k $的非空性，并且在大多数情况下，也存在一个通常平滑且预期维度的组件。作为一个应用，对于$ n $和$ k $的某些值，我们在任何曲线$ g \ ge ge 122 $的曲线上展示了标准brill的多余尺寸的组件 - 不b^k_ {2n，2n，2n（g-1）} $。我们为相干系统的模量空间获得了相似的结果。
The symplectic Brill--Noether locus ${\mathcal S}_{2n, K}^k$ associated to a curve $C$ parametrises stable rank $2n$ bundles over $C$ with at least $k$ sections and which carry a nondegenerate skewsymmetric bilinear form with values in the canonical bundle. This is a symmetric determinantal variety whose tangent spaces are defined by a symmetrised Petri map. We obtain upper bounds on the dimensions of various components of ${\mathcal S}_{2n, K}^k$. We show the nonemptiness of several ${\mathcal S}_{2n, K}^k$, and in most of these cases also the existence of a component which is generically smooth and of the expected dimension. As an application, for certain values of $n$ and $k$ we exhibit components of excess dimension of the standard Brill--Noether locus $B^k_{2n, 2n(g-1)}$ over any curve of genus $g \ge 122$. We obtain similar results for moduli spaces of coherent systems.
