发表机构
Massachusetts Institute of Technology（麻省理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文扩展穿孔对数Gromov-Witten理论在对数平展修正下的约化，应用于对数-轨道对应及分裂环面丛的重构，并引入带目标对数簇的双分歧环。
AI 中文摘要
我们扩展了作者先前关于穿孔对数Gromov-Witten理论在对数平展修正$\widetilde{X} \rightarrow X$下的行为的研究，给出了$\widetilde{X}$上的对数Gromov-Witten类用$X$上的对数Gromov-Witten类表达的公式，从而促进了对数方案$X$的任何修正$\widetilde{X}$的穿孔对数Gromov-Witten理论完全约化为$X$的穿孔对数Gromov-Witten理论。我们在两个情形中应用此结果。首先，我们证明了一个对数-轨道对应，将Gross和Siebert的典范壁结构的对数不变量与Tseng和You的相对量子上同调环中考虑的一类轨道不变量等同起来，并更一般地构造了一个从Gross和Siebert的内禀镜像代数$R_{(X,D)}$到适当的幂级数环的代数同态族。其次，我们证明了分裂环面丛的穿孔对数Gromov-Witten类可以有效地由基空间的穿孔对数Gromov-Witten类重构。第二个应用的额外输入是引入和研究带目标对数簇的双分歧环，推广了Janda-Pandharipande-Pixton-Zvonkine研究的带目标簇的双分歧环。
英文摘要
We expand upon a previous study conducted by the author on the behavior of punctured log Gromov-Witten theory under log étale modifications $\widetilde{X} \rightarrow X$, giving expressions for log Gromov-Witten classes on $\widetilde{X}$ in terms of log Gromov-Witten classes on $X$, facilitating a complete reduction of the punctured log Gromov-Witten theory of any modification $\widetilde{X}$ of an snc log scheme $X$ to the punctured log Gromov-Witten theory of $X$. We apply this result in two settings. First, we prove a log-orbifold correspondence equating the logarithmic invariants of the canonical wall structure of Gross and Siebert with a class of orbifold invariants considered in the relative quantum cohomology ring of Tseng and You, and more generally construct a family of algebra homomorphisms from the intrinsic mirror algebra $R_{(X,D)}$ of Gross and Siebert to appropriate power series rings. Second, we show the punctured log Gromov-Witten classes of split toric bundles are effectively reconstructed in terms of the punctured log Gromov-Witten classes of the base. Additional input for the second application is the introduction and study of double ramification cycles with target log variety, generalizing the double ramification cycles with target variety investigated by Janda-Pandharipande-Pixton-Zvonkine.
Comments53 pages, comments welcome
