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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.

Recovering an algebraic curve using its projections from different points. Applications to static and dynamic computational vision

Jeremy Yirmeyahu Kaminski, Michael Fryers, Mina Teicher (2005)

Journal of the European Mathematical Society

We study some geometric configurations related to projections of an irreducible algebraic curve embedded in 3 onto embedded projective planes. These configurations are motivated by applications to static and dynamic computational vision. More precisely, we study how an irreducible closed algebraic curve X embedded in 3 , of degree d and genus g , can be recovered using its projections from points onto embedded projective planes. The embeddings are unknown. The only input is the defining equation of...

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