algebraic geometry

On the -theoretic logarithmic double ramification class

arXiv:2607.13376

summary

The paper defines a K‑theoretic version of the logarithmic double ramification class, proves a product formula and GLₙ(ℤ)‑invariance, and provides an explicit expression using Grothendieck polynomials via a new K‑theoretic Thom–Porteous formula for vector bundles on algebraic stacks.

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 -theoretic Thom--Porteous formula for vector bundles on algebraic stacks.

54 pages, comments welcome

Topics & keywords

#double ramification cycle#k-theory#logarithmic geometry#grothendieck polynomials#thom-porteous formulak-theoretic double ramification classlogarithmic double ramificationproduct formulaGL_r(Z)-invariancealgebraic stacks