Comparison of motivic Chern classes and stable envelopes for cotangent bundles

TL;DR

This paper compares motivic Chern classes and K-theoretic stable envelopes for cotangent bundles of smooth projective varieties with torus actions, showing they coincide under certain conditions.

Contribution

It establishes the equivalence of motivic Chern classes and stable envelopes in specific geometric settings, clarifying their relationship.

Findings

Motivic Chern classes and stable envelopes coincide under certain assumptions.

The results apply to homogeneous spaces and similar varieties.

Provides a unified perspective on two important invariants in algebraic geometry.

Abstract

We consider a complex smooth projective variety equipped with an action of an algebraic torus with a finite number of fixed points. We compare the motivic Chern classes of Bia{\l}ynicki-Birula cells with the $K$-theoretic stable envelopes of cotangent bundle. We prove that under certain geometric assumptions satisfied e.g. by homogenous spaces these two notions coincide up to normalization.