Twisted motivic Chern class and stable envelopes

We present a definition of {\em twisted motivic Chern classes} for singular pairs $(X,Δ)$ consisting of a singular space $X$ and a $\mathbb Q$-Cartier divisor containing the singularities of $X$. The definition is a mixture of the construction of motivic Chern classes previously defined by Brasselet-Sch{ü}rmann-Yokura with the construction of multiplier ideals. The twisted motivic Chern classes are the limits of the elliptic classes defined by Borisov-Libgober. We show that with a suitable choice of the divisor $Δ$ the twisted motivic Chern classes satisfy the axioms of the stable envelopes in the K-theory. Our construction is an extension of the results proven by the first author for the fundamental slope.

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