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Rational equivalence on some families of plane curves

Josep M. Miret, Sebastián Xambó Descamps (1994)

Annales de l'institut Fourier

If V d , δ denotes the variety of irreducible plane curves of degree d with exactly δ nodes as singularities, Diaz and Harris (1986) have conjectured that Pic ( V d , δ ) is a torsion group. In this note we study rational equivalence on some families of singular plane curves and we prove, in particular, that Pic ( V d , 1 ) is a finite group, so that the conjecture holds for δ = 1 . Actually the order of Pic ( V d , 1 ) is 6 ( d - 2 ) d 2 - 3 d + 1 ) , the group being cyclic if d is odd and the product of 2 and a cyclic group of order 3 ( d - 2 ) ( d 2 - 3 d + 1 ) if d is even.

Real algebraic spaces

Andrew John Sommese (1977)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Relative Chow correspondences and the Griffiths group

Eric M. Friedlander (2000)

Annales de l'institut Fourier

A relativization of earlier constructions and Nori’s rational Lefschetz theorem enable interesting examples of the “topological filtration” on algebraic cycles.

Relative tangent cone of analytic curves

Danuta Ciesielska (1999)

Annales Polonici Mathematici

The purpose of this paper is to give a characterization of the relative tangent cone of two analytic curves in m with an isolated intersection.

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