Conjectural results for cohomological invariants of wild character varieties are obtained by counting curves in degenerate Calabi-Yau threefolds. A conjectural formula for E-polynomials is derived from the Gromov-Witten theory of local Calabi-Yau threefolds with normal crossing singularities. A refinement is also conjectured, generalizing existing results of Hausel, Mereb and Wong as well as recent joint work of Donagi, Pantev and the author for weighted Poincar\'e polynomials of wild character varieties.

中文翻译：

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局部曲线、野生特征品种和退化

通过对简并的 Calabi-Yau 三重曲线进行计数，可以获得野生性状品种上同调不变量的推测结果。E 多项式的推测公式是从具有正常交叉奇点的局部 Calabi-Yau 三重的 Gromov-Witten 理论推导出来的。还推测了改进，概括了 Hausel、Mereb 和 Wong 的现有结果以及 Donagi、Pantev 和作者最近对野生特性品种的加权 Poincar\'e 多项式的联合工作。