论文标题
生成一系列异国情调的未订购的配置空间
Generating series of classes of exotic un-ordered configuration spaces
论文作者
论文摘要
Yu。〜baryshnikov提出了空间$ x $的异国情调（有序）配置空间的概念。他给出了这些空间的（指数）生成一系列Euler特征的方程。在这里，我们考虑了这些空间的未命令类似物。对于$ x $，是一种复杂的Quasiprojective品种，我们为Grothendieck Ring $ k_0（{\ rm {var} _ {\ Mathbb {c}}}）$的复杂quasiprojective varieties的生成等式提供了这些配置空间的生成系列类别。答案是根据环$ k_0（{\ rm {var} _ {\ mathbb {c}}}}} $的（{\ rm {var} _ {\ rm {\ rm {\ rm {\ rm {\ rm {\ rm {\ rm {\ rm {\ rm {c}}} $）提出的答案。这给出了配置空间的一系列添加剂不变式生成的方程，例如hodge--deligne多项式和Euler特性。
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 $K_0({\rm{Var}_{\mathbb{C}}})$ of complex quasiprojective varieties. The answer is formulated in terms of the (natural) power structure over the ring $K_0({\rm{Var}_{\mathbb{C}}})$. This gives equations for the generating series of additive invariants of the configuration spaces such as the Hodge--Deligne polynomial and the Euler characteristic.
