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- W3149017654 abstract "Let k be a field, x = k[x1, …, xn] the polynomial ring in n variables over k, k(x) the field of fractions of k[x], and L a subfield of k(x) containing k. Hilbert’s fourteenth problem asks whether the k-algebra L ∩ k[x] is finitely generated. The answer to this problem is affirmative if ( operatorname *{mathrm{tr.deg}}_kLle 2) due to Zariski. In 1958, Nagata gave the first counterexample in the case ( operatorname *{mathrm{tr.deg}}_kL=4) and n = 32. In this chapter, we give a powerful method for constructing counterexamples to Hilbert’s fourteenth problem. Using this method, one can produce various kinds of counterexamples, including those in the case ( operatorname *{mathrm{tr.deg}}_kL=n=3)." @default.
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- W3149017654 date "2021-01-01" @default.
- W3149017654 modified "2023-09-26" @default.
- W3149017654 title "Counterexamples to Hilbert’s Fourteenth Problem" @default.
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- W3149017654 doi "https://doi.org/10.1007/978-3-030-60535-3_2" @default.
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