Summary
A cycle on an arbitrary algebraic variety (or scheme) X is a finite formal sum Σ n V [V] of (irreducible) subvarieties of X, with integer coefficients. A rational function r on any subvariety of X determines a cycle [div(r)]. Cycles differing by a sum of such cycles are defined to be rationally equivalent. Alternatively, rational equivalence is generated by cycles of the form [V(0)] − [V(∞)] for subvarieties V of X × ℙ1 which project dominantly to ℙ1. The group of rational equivalence classes on X is denoted A * X.
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© 1984 Springer-Verlag Berlin Heidelberg
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Fulton, W. (1984). Rational Equivalence. In: Intersection Theory. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-02421-8_2
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DOI: https://doi.org/10.1007/978-3-662-02421-8_2
Publisher Name: Springer, Berlin, Heidelberg
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