AI 中文总结
本文证明Welschinger不变量是全体亏格曲线计数中按边界Conway多项式加权的最低阶项，并指出该计数是skein值曲线计数的特化，且无需4-链和向量场即可定义。
AI 中文摘要
Welschinger证明了在辛6流形中，具有Lagrangian边界的连通全纯圆盘计数，在满足至少一个边界约束时，可以通过用某些“自链环”数加权的非连通圆盘计数进行修正，从而使其成为不变量。我们证明了他的不变量是全体亏格曲线计数中的最低阶项，其中曲线按其边界的Conway多项式加权。这反过来又是 skein 值曲线计数的一个特化，但可以在不使用该设置中的4-链和向量场的情况下定义。
英文摘要
Welschinger showed that counts of connected holomorphic disks with Lagrangian boundary in symplectic 6-manifolds, meeting at least one boundary constraint, can be made invariant by correcting them with counts of disconnected disks weighted by certain "self-linking" numbers. We show his invariant is the lowest order term in an all-genus curve count where curves are weighted by the Conway polynomials of their boundaries. This in turn is a specialization of the skein-valued curve count, but can be defined without the 4-chain and vector field used in that setup.
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