Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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 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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