Comparison of motivic Chern classes and stable envelopes for cotangent bundles

2020/06/03 by Jakub Koncki, Koncki, Jakub
Mathematics · #14C17 #14M15 #19L47 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2006.02403

openalex publication_date 2020/06/03 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

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 Białynicki-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.

Related

• Motivic Chern classes of cones
• Chern classes of proalgebraic varieties and motivic measures
• Twisted motivic Chern class and stable envelopes
• Motivic Chern classes of configuration spaces
• Hecke algebra action on twisted motivic Chern classes and K-theoretic stable envelopes