The Fulton-MacPherson compactification is not a Mori dream space
نویسندگان
چکیده
We show that the Fulton-MacPherson compactification of configuration space n distinct labeled points in certain varieties arbitrary dimension d, including projective space, is not a Mori dream for larger than $$d + 8$$ .
منابع مشابه
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...
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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.
متن کامل1 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...
متن کاملChow 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)....
متن کاملEvery Hausdorff Compactification of a Locally Compact Separable Space Is a Ga Compactification
1. I n t r o d u c t i o n . In [4], De Groot and Aarts constructed Hausdorff compactifications of topological spaces to obtain a new intrinsic characterization of complete regularity. These compactifications were called GA compactifications in [5] and [7]. A characterization of complete regularity was earlier given by Fr ink [3], by means of Wallman compactifications, a method which led to the...
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ژورنال
عنوان ژورنال: Mathematische Zeitschrift
سال: 2022
ISSN: ['1432-1823', '0025-5874']
DOI: https://doi.org/10.1007/s00209-022-03145-x