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- Nagata's_conjecture_on_curves abstract "In mathematics, the Nagata conjecture on curves, named after Masayoshi Nagata, governs the minimal degree required for a plane algebraic curve to pass through a collection of very general points with prescribed multiplicities. Nagata arrived at the conjecture via work on the 14th problem of Hilbert, which asks whether the invariant ring of a linear group action on the polynomial ring k[x1, ..., xn] over some field k is finitely generated. Nagata published the conjecture in a 1959 paper in the American Journal of Mathematics, in which he presented a counterexample to Hilbert's 14th problem:Nagata Conjecture. Suppose p1, ..., pr are very general points in P2 and that m1, ..., mr are given positive integers. Then for r > 9 any curve C in P2 that passes through each of the points pi with multiplicity mi must satisfyThe only case when this is known to hold is when r is a perfect square, which was proved by Nagata. Despite much interest the other cases remain open. A more modern formulation of this conjecture is often given in terms of Seshadri constants and has been generalised to other surfaces under the name of the Nagata–Biran conjecture.The condition r > 9 is easily seen to be necessary. The cases r > 9 and r ≤ 9 are distinguished by whether or not the anti-canonical bundle on the blowup of P2 at a collection of r points is nef.".
- Nagata's_conjecture_on_curves wikiPageID "5140476".
- Nagata's_conjecture_on_curves wikiPageRevisionID "606099086".
- Nagata's_conjecture_on_curves hasPhotoCollection Nagata's_conjecture_on_curves.
- Nagata's_conjecture_on_curves subject Category:Algebraic_curves.
- Nagata's_conjecture_on_curves subject Category:Conjectures.
- Nagata's_conjecture_on_curves type Abstraction100002137.
- Nagata's_conjecture_on_curves type AlgebraicCurves.
- Nagata's_conjecture_on_curves type Attribute100024264.
- Nagata's_conjecture_on_curves type Cognition100023271.
- Nagata's_conjecture_on_curves type Concept105835747.
- Nagata's_conjecture_on_curves type Conjectures.
- Nagata's_conjecture_on_curves type Content105809192.
- Nagata's_conjecture_on_curves type Curve113867641.
- Nagata's_conjecture_on_curves type Hypothesis105888929.
- Nagata's_conjecture_on_curves type Idea105833840.
- Nagata's_conjecture_on_curves type Line113863771.
- Nagata's_conjecture_on_curves type PsychologicalFeature100023100.
- Nagata's_conjecture_on_curves type Shape100027807.
- Nagata's_conjecture_on_curves type Speculation105891783.
- Nagata's_conjecture_on_curves comment "In mathematics, the Nagata conjecture on curves, named after Masayoshi Nagata, governs the minimal degree required for a plane algebraic curve to pass through a collection of very general points with prescribed multiplicities. Nagata arrived at the conjecture via work on the 14th problem of Hilbert, which asks whether the invariant ring of a linear group action on the polynomial ring k[x1, ..., xn] over some field k is finitely generated.".
- Nagata's_conjecture_on_curves label "Nagata's conjecture on curves".
- Nagata's_conjecture_on_curves sameAs m.0d4m_q.
- Nagata's_conjecture_on_curves sameAs Q6958658.
- Nagata's_conjecture_on_curves sameAs Q6958658.
- Nagata's_conjecture_on_curves sameAs Nagata's_conjecture_on_curves.
- Nagata's_conjecture_on_curves wasDerivedFrom Nagata's_conjecture_on_curves?oldid=606099086.
- Nagata's_conjecture_on_curves isPrimaryTopicOf Nagata's_conjecture_on_curves.