Algebraic curve

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Translations
curva algebrica
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Mathematicians survey new applications of algebraic curves that the recent development of computational techniques and significant growth in computer power have made possible.
Grau, "Coexistence of limit cycles and invariant algebraic curves for a Kukles system," Nonlinear Analysis.
Meilhan, A linking invariant for algebraic curves, arXiv:1602.04916.
As an intermediate step towards the third result, we also show that for a fixed family of plane algebraic curves with s degrees of freedom, every set of n points in the plane has a subset of [OMEGA]([n.sup.1-1/s]) points incident to a single curve, or a subset of [OMEGA]([n.sup.1/s]) points such that at most s of them lie on a curve.
Hilbert's 16th problem has two parts and its first part is on the topology of algebraic curves and surfaces.
One particularly nice way of studying general parametric cubics can be found in [3] which treats them as general algebraic curves, determines their properties, and then specializes the results to the family of general parametric cubics.
Other topics include counting algebraic curves with tropical geometry, block triangular bilinear forms and braid group action, the topicalization method in cluster algebras, and an application of the max-plus spectral theory to an ultradiscrete analogue of the Lax pair.
HARIS, Real algebraic curves, Annales scientifiques de l'ENS, 4 eme sErie, tome 14, no.

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