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- Title
Chebyshev curves, free resolutions and rational curve arrangements.
- Authors
DIMCA, ALEXANDRU; STICLARU, GABRIEL
- Abstract
First we construct a free resolution for the Milnor (or Jacobian) algebra M(f) of a complex projective Chebyshev plane curve 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 ≥ 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.
- Subjects
CHEBYSHEV systems; FREE resolutions (Algebra); SMOOTHNESS of functions; FACTORIZATION; MATHEMATICAL analysis
- Publication
Mathematical Proceedings of the Cambridge Philosophical Society, 2012, Vol 153, Issue 3, p385
- ISSN
0305-0041
- Publication type
Article
- DOI
10.1017/S0305004112000138