发表机构
Institute of Mathematics, AMSS, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究局部对数Calabi-Yau 4-折叠的对数DT不变量，构造相对与族理论并证明退化公式，结合对数配边显式计算零维不变量。
AI 中文摘要
本文研究了具有简单正规交叉除子的局部对数Calabi-Yau 4-折叠的对数Donaldson-Thomas不变量。利用Khan-Kinjo-Park-Safronov宣布的移位Lagrangian类的族版本，我们为曲线的对数Hilbert概形构造了相对和族对数$\mathsf{DT}_4$-理论，并证明了退化公式。对于点的对数Hilbert概形，我们构造了虚拟类并在Chow群中证明了退化公式；特别地，它不依赖于移位Lagrangian类。最后，将我们的退化公式与对数配边相结合，我们显式计算了局部曲面snc对零维对数$\mathsf{DT}_4$-不变量。
英文摘要
In this paper, we study logarithmic Donaldson-Thomas invariants for local log Calabi-Yau $4$-folds with simple normal crossing divisors. Using the family version of shifted Lagrangian classes announced by Khan-Kinjo-Park-Safronov, we construct relative and family logarithmic $\mathsf{DT}_4$-theories for logarithmic Hilbert schemes of curves, and prove a degeneration formula. For logarithmic Hilbert schemes of points, we construct virtual classes and prove a degeneration formula in Chow groups; in particular, it is independent of shifted Lagrangian classes. Finally, combining our degeneration formula with logarithmic cobordism, we explicitly compute the zero-dimensional logarithmic $\mathsf{DT}_4$-invariants for local surface snc pairs.
Comments62 pages. v2: added a reference and made minor improvements to the exposition
