Twisted motivic Chern class and stable envelopes

Abstract

We present a definition of {\em twisted motivic Chern classes} for singular pairs $(X,\Delta )$ 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 $\Delta$ 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.

to appear in Advances in Mathematics