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- W24603076 abstract "We study two variants of the following question: Given two finitely generated subalgebras R_1, R_2 of C[x_1, ldots, x_n], is their intersection also finitely generated? We show that the smallest value of $n$ for which there is a counterexample is 2 in the general case, and 3 in the case that R_1 and R_2 are integrally closed. We also explain the relation of this question to the problem of constructing algebraic compactifications of C^n and to the moment problem on semialgebraic subsets of R^n. The counterexample for the general case is a simple modification of a construction of Neena Gupta, whereas the counterexample for the case of integrally closed subalgebras uses the theory of normal analytic compactifications of C^2 via key forms of valuations centered at infinity." @default.
- W24603076 created "2016-06-24" @default.
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- W24603076 date "2013-01-12" @default.
- W24603076 modified "2023-09-27" @default.
- W24603076 title "When is the intersection of two finitely generated subalgebras of a polynomial ring also finitely generated" @default.
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