Motivic Chern classes of configuration spaces

Abstract

We calculate the equivariant motivic Chern class for configuration space of smooth variety and the space of vectors with different directions. We prove the formulas for generating series of these classes. We generalize the localization theorems results about BB-decomposition to acquire some stability for the motivic Chern classes of configuration spaces.

Comparison of motivic Chern classes and stable envelopes for cotangent bundles

“…Let F ⊂ X σ H be a component of the fixed points set of σ H which contains F ′ . Proposition 4.3 and theorem 4.4 from [Kon19] implies that lim…”

“…Then the limit map is defined on the subring K A/σ H (pt)[t][y, y −1 ] by killing all positive powers of t. For technical details, extension to the localised K-theory and proof of being well defined see [Kon19] section 4.…”

“…[CG10] theorem 5.11.7) and above properties. For examples of computation see [FRW18b,Kon19]. In the paper [FRW18b] (see also [FRW18a]) it was found that for G-equivariant varieties with finite number of orbits the motivic Chern classes mC G of G orbits satisfy axioms similar to those of the stable envelopes.…”

“…Our main technical tool is study of limits of Laurent polynomials (of one or many variables). The limit technique was investigated both for motivic Chern classes [Web17,FRW18b,Kon19] as well as for stable envelopes [SZZ17,Oko17]. We use it mainly to prove various containments of Newton polytopes.…”