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A Survey of Counterexamples to Hilbert's Fourteenth Problem

Freudenburg, Gene (2001)

Serdica Mathematical Journal

We survey counterexamples to Hilbert’s Fourteenth Problem, beginning with those of Nagata in the late 1950s, and including recent counterexamples in low dimension constructed with locally nilpotent derivations. Historical framework and pertinent references are provided. We also include 8 important open questions.

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