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Article Dans Une Revue Mathematical Proceedings of the Cambridge Philosophical Society Année : 2012

Chebyshev curves, free resolutions and rational curve arrangements

Alexandru Dimca
Gabriel Sticlaru
  • Fonction : Auteur

Résumé

First we construct a free resolution for the Milnor (or Jacobian) algebra $M(f)$ of a complex projective Chebyshev plane curve $\CC_d:f=0$ of degree $d$. In particular, this resolution implies that the dimensions of the graded components $M(f)_k$ are constant for $k \geq 2d-3.$ Then we show that the Milnor algebra of a nodal plane curve $C$ has such a behaviour if and only if all the irreducible components of $C$ are rational. For the Chebyshev curves, all of these components are in addition smooth, hence they are lines or conics and explicit factorizations are given in this case.

Dates et versions

hal-00940200 , version 1 (31-01-2014)

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Alexandru Dimca, Gabriel Sticlaru. Chebyshev curves, free resolutions and rational curve arrangements. Mathematical Proceedings of the Cambridge Philosophical Society, 2012, 153, pp.385-397. ⟨10.1017/S0305004112000138⟩. ⟨hal-00940200⟩
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