On the $K$-theoretic logarithmic double ramification class

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

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.

Disclosure

“rr, and Mark Shimozono for discussions about Grothendieck polynomials. These results were presented at IMJ-PRG and in ICTS-TIFR. We thank A. Chiodo, P. Georgieva, C. Ravi and B. Sreedhar for inviting us to deliver a talk on this topic. AI (ChatGPT and Claude) made us aware of the Eagon–Northcott complex, created the glossary, checked for typos, and substantially helped with editing. The proofs of Lemmas B.5, B.6 were refined in collaboration with AI upon noticing a mistake in an ear”
PDF page 8

Classification: Proof ideas or individual proof-step assistance
Multiplier: 8
Verified: 2026-08-23T18:55:29.904990Z

Structural counts

Pages 54 pdf

Theorems 13 source

Lemmas 14 source

Propositions 10 source

Corollaries 6 source

Definitions 31 source

Displayed equations 234 source

Bibliography entries 144 source

Appendix pages 54 estimated

Count notes

Source counts use the expanded primary TeX file main.tex.
Appendix pages include the first PDF page with an explicit Appendix heading through the final page.