关于\(K\)理论对数双分歧类
On the $K$-theoretic logarithmic double ramification class
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中文总结 AI 辅助
研究关于对数双分歧类，通过构造\(K\)理论对数双分歧类，证明其乘积公式与\(\mathrm{GL}_r(\mathbb Z)\)不变性，还借助新公式给出基于格罗滕迪克多项式的显式公式。
中文摘要 AI 辅助
对数双分歧循环是一族曲线上线丛纤维平凡的轨迹的虚拟基本类。我们构造了一个\(K\)理论对数双分歧类，证明了一个乘积公式和一个\(\mathrm{GL}_r(\mathbb Z)\)不变性性质。通过代数栈上向量丛的新的\(K\)理论托姆 - 波特斯公式，我们还根据格罗滕迪克多项式给出了该类的显式公式。
英文摘要
The logarithmic double ramification cycle is the virtual fundamental class of the locus where a line bundle on a family of curves is fiberwise trivial. We construct a K-theoretic logarithmic double ramification class and prove a product formula and a \(\mathrm{GL}_r(\mathbb Z)\)-invariance property. We also give an explicit formula for this class in terms of a Grothendieck polynomial via a novel $K$-theoretic Thom--Porteous formula for vector bundles on algebraic stacks.
