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arXiv · 2607.13376

On the $K$-theoretic logarithmic double ramification class

Kamyar Amini·You-Cheng Chou·Leo Herr·David Holmes·Irit Huq-Kuruvilla·Yuan-Pin Lee
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Abstract

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.

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Kamyar Amini, You-Cheng Chou, Leo Herr, David Holmes, Irit Huq-Kuruvilla, Yuan-Pin Lee. 2026-07-15. On the $K$-theoretic logarithmic double ramification class. https://arxiv.org/abs/2607.13376

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