Twisted motivic Chern class and stable envelopes

Abstract

We present a definition of twisted motivic Chern classes for singulars pairs (X, ∆) consisting of a singular space X and a Q-Cartier divisor containing the singularities of X. The definition is a mixture of the construction of motivic Chern classes previously defined by Brasselet-Schürmann-Yokura with the construction of multiplier ideals. The twisted motivic Chern classes are the limits of the the elliptic classes defined by Borisov-Libgober. We show that with a suitable choice of the divisor ∆ the twisted motivic Chern classes satisfy the axioms of the stable envelopes in K-theory. Our construction is an extension of the results proven by the first author for the fundamental slope.Both authors are supported by NCN grant 2016/23/G/ST1/04282 (Beethoven 2).