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.

与曲线C参数相关的辛Brill–Noether位点\（{{{\ mathcal {S}}}} _ {2n，K} ^ k \）在C上具有至少k个截面且携带至少k个截面的2 n级稳定束在规范束中具有值的非退化的偏对称双线性形式。这是一个对称的行列式变体，其切线空间由对称的陪替氏图定义。我们获得\（{{{\ mathcal {S}}}} _ {2n，K} ^ k \）的各个分量的维度的上限。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，还存在通常平滑且具有预期尺寸的组件。作为应用，对于n和k的某些值，我们在属（\ g的任何一条曲线上都展示了标准Brill–Noether位点\（B ^ k_ {2n，2n（g-1）} \）的超出维度的分量。ge 122 \）。对于相干系统的模空间，我们获得了相似的结果。