On finite generation of symbolic Rees rings of space monomial curves and existence of negative curves

DOI10.1016/j.jalgebra.2008.08.015zbMath1188.14021arXiv0801.3896OpenAlexW2066194247MaRDI QIDQ2654065

Kazuhiko Kurano, Naoyuki Matsuoka

Publication date: 15 January 2010

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0801.3896

zbMATH Keywords

symbolic Rees ringCowsik's questionHilbert's fourteen problemspace monomial curve

Mathematics Subject Classification ID

Plane and space curves (14H50) Actions of groups on commutative rings; invariant theory (13A50) Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics (13A30)

Related Items (14)

Multiplicities of Monomial Space Curves with Non-Noetherian Symbolic Blowups ⋮ Symbolic Rees Algebras ⋮ Some necessary and sufficient condition for finite generation of symbolic Rees rings ⋮ On Intrinsic Negative Curves ⋮ Saturations of powers of certain determinantal ideals ⋮ Equations of negative curves of blow-ups of Ehrhart rings of rational convex polygons ⋮ Asymptotic regularity of powers of ideals of points in a weighted projective plane ⋮ Divisors on rational normal scrolls ⋮ Mori dreamness of blowups of weighted projective planes ⋮ On curves with high multiplicity on \(\mathbb{P}(a,b,c)\) for \(\min(a,b,c) \leq 4\) ⋮ Curves generating extremal rays in blowups of weighted projective planes ⋮ Symbolic blowup algebras and invariants of certain monomial curves in an affine space ⋮ Constructing non-Mori dream spaces from negative curves ⋮ \(\overline{M}_{0,n}\) is not a Mori dream space

Cites Work

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• Non-Cohen-Macaulay Symbolic Blow-Ups for Space Monomial Curves and Counterexamples to Cowsik's Question
• Symbolic algebras of monomial primes.
• Mori dream spaces and GIT.

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