Generating series of classes of exotic un-ordered configuration spaces

DOI10.1134/S003744662301007XarXiv2203.10798WikidataQ121663556 ScholiaQ121663556MaRDI QIDQ6394213

Sabir M. Gusein-Zade

Publication date: 21 March 2022

Abstract: A notion of exotic (ordered) configuration spaces of points on a space $X$ was suggested by Yu.~Baryshnikov. He gave equations for the (exponential) generating series of the Euler characteristics of these spaces. Here we consider un-ordered analogues of these spaces. For $X$ being a complex quasiprojective variety, we give equations for the generating series of classes of these configuration spaces in the Grothendieck ring $K_0(m{Var}_{mathbbC})$ of complex quasiprojective varieties. The answer is formulated in terms of the (natural) power structure over the ring $K_0(m{Var}_{mathbbC})$. This gives equations for the generating series of additive invariants of the configuration spaces such as the Hodge--Deligne polynomial and the Euler characteristic.

Mathematics Subject Classification ID

Applications of methods of algebraic (K)-theory in algebraic geometry (14C35)

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