High Quality Content by WIKIPEDIA articles! In mathematics, the Nagata conjecture on curves governs the minimal degree required for a plane algebraic curve to pass though a collection of very general points with prescribed multiplicity. Nagata arrived at the conjecture via work on the 14th problem of Hilbert, which asks whether the invariant ring of a linear group action on the polynomial ring k[x_1, ldots x_n] over some field k is finitely generated. Nagata published the conjecture in a 1959 paper in the American Journal of Mathematics, in which he presented a counterexample to Hilbert's 14th problem.

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