Positive characteristic finite generation of symbolic Rees algebras and Roberts' counterexamples to the fourteenth problem of Hilbert

DOI10.3836/tjm/1270128498zbMath0797.13002OpenAlexW2054228423WikidataQ124830131 ScholiaQ124830131MaRDI QIDQ1321754

Kazuhiko Kurano

Publication date: 13 October 1994

Published in: Tokyo Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3836/tjm/1270128498

zbMATH Keywords

Hilbert's 14th problemfinite generation of the symbolic Rees ringprime ideal in a polynomial ring

Mathematics Subject Classification ID

Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Commutative Noetherian rings and modules (13E05) Ideals and multiplicative ideal theory in commutative rings (13A15) Commutative rings and modules of finite generation or presentation; number of generators (13E15) Characteristic (p) methods (Frobenius endomorphism) and reduction to characteristic (p); tight closure (13A35) Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics (13A30)

Related Items (10)

Symbolic Rees Algebras ⋮ A simple proof of Nowicki's conjecture on the kernel of an elementary derivation ⋮ On finite generation of symbolic Rees rings of space monomial curves and existence of negative curves ⋮ On the finite generation of additive group invariants in positive characteristic ⋮ Weitzenböck derivations of free metabelian Lie algebras ⋮ The Nowicki conjecture for free metabelian Lie algebras ⋮ Equations of negative curves of blow-ups of Ehrhart rings of rational convex polygons ⋮ A generalization of Roberts' counterexample to the fourteenth problem of Hilbert ⋮ Infinitely generated symbolic Rees algebras over finite fields ⋮ A linear counterexample to the Fourteenth Problem of Hilbert in dimension eleven

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