We construct invariants for any closed semipositive symplectic manifold which count rational curves satisfying tangency constraints to a local divisor. More generally, we introduce invariants involving multibranched local tangency constraints. We give a formula describing how these invariants arise as point constraints are pushed together in dimension four, and we use this to recursively compute all of these invariants in terms of Gromov–Witten invariants of blowups. As a key tool, we study analogous invariants which count punctured curves with negative ends on a small skinny ellipsoid.

中文翻译：

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计算具有局部相切约束的曲线

我们为任何封闭的半正辛流形构造不变量，它计算满足局部除数的切线约束的有理曲线。更一般地说，我们引入了涉及多分支局部相切约束的不变量。我们给出了一个公式来描述当点约束在四维中被推到一起时这些不变量是如何产生的，并且我们使用它来递归地计算所有这些不变量的 Gromov–Witten 不变量的爆破。作为一个关键工具，我们研究了类似的不变量，这些不变量计算了在一个小的瘦椭圆体上具有负端的穿孔曲线。