ИСТИНА

The notion of exotic (ordered) configuration spaces of points on a space $X$ was introduced by Yu.Baryshnikov. They are generalizations of $X^k$ and $X^k\setminus\Delta$, where $\Delta$ is the large diagonal in $X^n$ consisting of $n$-tuples $(x_1,\ldots, x^k)\in X^n$ of points with at least two coinciding ones. We consider unordered analogues of these spaces. The simplest of them (``non-exotic'' ones) are the symmetic powers $S^kX=X^k/S_k$ and the configuration spaces $\Lambda^kX=(X^k\setminus\Delta)/S_k$, where $S_k$ is the group of permutations on $k$ elements. In general, an exotic configuration space on $X$ is the configuration space of points colored by several colors with a fixed list of permitted collisions. The generating series of the Euler characteristics of the symmetric powers $S^kX$ is given by the Macdonald equation: $$ \sum\limits_{k=0}^{\infty}\chi(S^kX)\cdot t^k=(1-t)^{-\chi(X)}. $$ We give an analogue of this equation for exotic configuration spaces. For a space $X$ being a complex quasiprojective variety, the exotic configuration spaces are complex quasiprojective varieties as well. Thus one can consider their classes in the Grothendieck ring of $K_0({\rm Var}_{C})$ of complex quasiprojective varieties. We give a Macdonald type equation for the generating series of classes of exotic configulation spaces. The answer is formulated in terms of the geometric power structure over the Grothendieck ring $K_0({\rm Var}_{C})$. Specializations of this equation give equations for generating series of additive and multiplicative invariants of the exotic configuration spaces, e.g., of Hodge-Deligne polynomials.