We provide an inductive algorithm computing Gromov–Witten invariants in all genera with arbitrary insertions of all smooth complete intersections in projective space. We also prove that all Gromov–Witten classes of all smooth complete intersections in projective space belong to the tautological ring of the moduli space of stable curves. The main idea is to show that invariants with insertions of primitive cohomology classes are controlled by their monodromy and by invariants defined without primitive insertions but with imposed nodes in the domain curve. To compute these nodal Gromov–Witten invariants, we introduce the new notion of nodal relative Gromov–Witten invariants. We then prove a nodal degeneration formula and a relative splitting formula. These results for nodal relative Gromov–Witten theory are stated in complete generality and are of independent interest.

中文翻译：

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通过节点不变量的完全相交的 Gromov-Witten 理论

我们提供了一种归纳算法来计算所有属中的 Gromov–Witten 不变量，并在射影空间中任意插入所有平滑的完全交集。我们还证明了射影空间中所有光滑完全交集的所有 Gromov-Witten 类都属于稳定曲线模空间的重言式环。主要思想是表明具有插入本原上同调类的不变量由它们的单值性以及由没有本原插入定义但在域曲线中具有强加节点的不变量控制。为了计算这些节点 Gromov-Witten 不变量，我们引入了节点相对 Gromov-Witten 不变量的新概念。然后我们证明了一个节点退化公式和一个相对分裂公式。