Curvas nodais maximais via curvas de Fermat
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2009-01-01
Autores
Profilo, Stanley
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Universidade Federal do Espírito Santo
Resumo
We study the rational projective nodal plane curves in the projective plane P2(C) by using the Fermat curve Fn : Xn+Y n+Zn = 0. We deal with the theory of dual curves in the projective plane and a special type of group action of Zn x Zn on the Fermat curve and its dual to construct, for any positive integer n maior ou igual a 3, a rational nodal plane curve of degree equal to n -1. A rational nodal plane curve is a projective rational plane curve (that is, a genus zero curve) that presents as singularities only nodal points, that is, singularities of multiplicity two with distinct tangents. The basic reference is the paper "On Fermat Curves and Maximal Nodal Curves"by Matsuo OKA published in Michigan Math. Journal, v.53. in 2005.
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Álgebra , Curvas nodais
Citação
PROFILO, Stanley. Curvas nodais maximais via curvas de Fermat. 2009. 53 f. Dissertação (Mestrado em Matemática) - Programa de Pós-Graduação em Matemática, Universidade Federal do Espírito Santo, Vitória, 2009.