On the power structure over the Grothendieck ring of varieties and its applications. (English. Russian original) Zbl 1222.14007
Proc. Steklov Inst. Math. 258, 53-64 (2007); translation from Tr. Mat. Inst. Steklova 258, 58-69 (2007).
Summary: We discuss the notion of a power structure over a ring and the geometric description of the power structure over the Grothendieck ring of complex quasi-projective varieties and show some examples of applications to generating series of classes of configuration spaces (for example, nested Hilbert schemes of J. Cheah [Math. Z. 227, No. 3, 479–504 (1998; Zbl 0890.14003); J. Algebr. Geom. 5, No. 3, 479–511 (1996; Zbl 0889.14001)]) and wreath product orbifolds.
MSC:
| 14C05 | Parametrization (Chow and Hilbert schemes) |
| 16E20 | Grothendieck groups, \(K\)-theory, etc. |
| 14C35 | Applications of methods of algebraic \(K\)-theory in algebraic geometry |
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