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Computing Chow groups. (English) Zbl 0663.14001

Algebraic geometry, Proc. Conf., Sundance/Utah 1986, Lect. Notes Math. 1311, 220-234 (1988).
[For the entire collection see Zbl 0635.00006.]
Let X be an algebraic k-scheme of finite type with a cellular decomposition \(\{Z_{ij}\}\) as defined by W. Fulton [(“Intersection theory” (Berlin 1984; Zbl 0541.14005)] and k an algebraically closed field. The authors give a description of the Chow groups of X, they show that they are free with basis the closure of the cells of the decomposition, in any characteristic. In the case of a fibration \(f:\quad X'\to X,\) such that \(f^{-1}(Z_{ij})=Z_{ij}\times F\) where F is a fixed scheme, they give a method to compute the Chow groups of X’ in terms of the Chow groups of X and F.
Reviewer: A.Papantonopoulou

MSC:

14C05 Parametrization (Chow and Hilbert schemes)
14C17 Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry
14D99 Families, fibrations in algebraic geometry