The Chow ring of a Fulton-MacPherson compactification

The Chow Ring of Relative Fulton–macpherson Space

Suppose that X is a nonsingular variety and D is a nonsingular proper subvariety. Configuration spaces of distinct and non-distinct n points in X away from D were constructed by the author and B. Kim in [4] by using the method of wonderful compactification. In this paper, we give an explicit presentation of Chow motives and Chow rings of these configuration spaces.

Chow Motive of Fulton-macpherson Configuration Spaces and Wonderful Compactifications

The purpose of this article is to study the Chow groups and Chow motives of the so-called wonderful compactifications of an arrangement of subvarieties, in particular the Fulton-MacPherson configuration spaces. All the varieties in the paper are over an algebraically closed field. Let Y be a nonsingular quasi-projective variety. Let S be an arrangement of subvarieties of Y (cf. Definition 2.2)....

8 Fulton - MacPherson compactification , cyclohedra , and the polygonal pegs problem

The cyclohedron Wn, known also as the Bott-Taubes polytope, arises both as the polyhedral realization of the poset of all cyclic bracketings of the word x1x2 . . . xn and as an essential part of the Fulton-MacPherson compactification of the configuration space of n distinct, labelled points on the circle S1. The “polygonal pegs problem” asks whether every simple, closed curve in the plane or in...

1 1 N ov 2 00 8 Fulton - MacPherson compactification , cyclohedra , and the polygonal pegs problem

The cyclohedron Wn, known also as the Bott-Taubes polytope, arises both as the polyhedral realization of the poset of all cyclic bracketings of the word x1x2 . . . xn and as an essential part of the Fulton-MacPherson compactification of the configuration space of n distinct, labelled points on the circle S1. The “polygonal pegs problem” asks whether every simple, closed curve in the plane or in...

The Chow-Witt ring