Characteristic classes of orbit stratifications, the axiomatic approach
Autor: | Feher, Laszlo M., Rimanyi, Richard, Weber, Andrzej |
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Rok vydání: | 2018 |
Předmět: | |
Druh dokumentu: | Working Paper |
Popis: | Consider a complex algebraic group $G$ acting on a smooth variety $M$ with finitely many orbits, and let $\Omega$ be an orbit. The following three invariants of $\Omega\subset M$ can be characterized axiomatically: (1) the equivariant fundamental class $[\overline{\Omega}, M]\in H^*_G(M)$, (2) the equivariant Chern-Schwartz-MacPherson class $c(\Omega, M)\in H^*_G(M)$, and (3) the equivariant motivic Chern class $mC(\Omega, M) \in K_G(M)[y]$. The axioms for Chern-Schwartz-MacPherson and motivic Chern classes are motivated by the axioms for cohomological and K-theoretic stable envelopes of Okounkov and his coauthors. For $M$ a flag variety and $\Omega$ a Schubert cell---an orbit of the Borel group acting---this implies that CSM and MC classes coincide with the weight functions studied by Rimanyi-Tarasov-Varchenko. In this paper we review the general theory and illustrate it with examples. Comment: 5 figures |
Databáze: | arXiv |
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