Let C be a smooth projective curve and W a symplectic bundle over C. Let $L{Q}_e(W)$ be the Lagrangian Quot scheme parametrizing Lagrangian subsheaves $E\subset W$ of degree e. We give a closed formula for intersection numbers on $L{Q}_e(W)$. As a special case, for $g\ge 2$, we compute the number of Lagrangian subbundles of maximal degree of a general stable symplectic bundle, when this is finite. This is a symplectic analogue of Holla's enumeration of maximal subbundles in [14].

中文翻译：

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计算代数曲线上的最大拉格朗日子束

令C为光滑的射影曲线，令W为C上的辛束。让$\mathrm{大号}{问}_{Ë}（\mathrm{w\; ^}）$ 是参数化拉格朗日子滑轮的拉格朗日报价方案 $E\subset \mathrm{w\; ^}$度为e。我们给出交点数的封闭公式$\mathrm{大号}{问}_{Ë}（\mathrm{w\; ^}）$。作为一种特殊情况，$G\ge \mathrm{2个}$，当它是有限的时，我们计算一般稳定辛束的最大程度的拉格朗日子束的数量。这是Holla [14]中最大子束枚举的辛模拟。