Masayoshi Nagata
Encyclopedia
Masayoshi Nagata was a Japan
ese mathematician
, known for his work in the field of commutative algebra
.
In 1959 he brought forward a counterexample
to the general case of Hilbert's fourteenth problem
on invariant theory
.
One of his students at Kyoto University
was Shigefumi Mori
.
Nagata's conjecture on curves
concerns the minimum degree of a plane curve
specified to have given multiplicities at given points; see also Seshadri constant
. Nagata's conjecture on automorphisms concerns the existence of wild automorphisms of polynomial algebras in three variables. Recent work has solved this latter problem in the affirmative.
Japan
Japan is an island nation in East Asia. Located in the Pacific Ocean, it lies to the east of the Sea of Japan, China, North Korea, South Korea and Russia, stretching from the Sea of Okhotsk in the north to the East China Sea and Taiwan in the south...
ese mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, known for his work in the field of commutative algebra
Commutative algebra
Commutative algebra is the branch of abstract algebra that studies commutative rings, their ideals, and modules over such rings. Both algebraic geometry and algebraic number theory build on commutative algebra...
.
In 1959 he brought forward a counterexample
Counterexample
In logic, and especially in its applications to mathematics and philosophy, a counterexample is an exception to a proposed general rule. For example, consider the proposition "all students are lazy"....
to the general case of Hilbert's fourteenth problem
Hilbert's fourteenth problem
In mathematics, Hilbert's fourteenth problem, that is, number 14 of Hilbert's problems proposed in 1900, asks whether certain rings are finitely generated....
on invariant theory
Invariant theory
Invariant theory is a branch of abstract algebra dealing with actions of groups on algebraic varieties from the point of view of their effect on functions...
.
One of his students at Kyoto University
Kyoto University
, or is a national university located in Kyoto, Japan. It is the second oldest Japanese university, and formerly one of Japan's Imperial Universities.- History :...
was Shigefumi Mori
Shigefumi Mori
-References:*Heisuke Hironaka, Fields Medallists Lectures, Michael F. Atiyah , Daniel Iagolnitzer ; World Scientific Publishing, 2007. ISBN 9810231172...
.
Nagata's conjecture on curves
Nagata's conjecture on curves
In mathematics, the Nagata conjecture on curves, named after Masayoshi Nagata, governs the minimal degree required for a plane algebraic curve to pass though a collection of very general points with prescribed multiplicity...
concerns the minimum degree of a plane curve
Plane curve
In mathematics, a plane curve is a curve in a Euclidean plane . The most frequently studied cases are smooth plane curves , and algebraic plane curves....
specified to have given multiplicities at given points; see also Seshadri constant
Seshadri constant
In algebraic geometry, a Seshadri constant is an invariant of an ample line bundle L at a point P on an algebraic variety. It was introduced by Demailly to measure a certain rate of growth, of the tensor powers of L, in terms of the jets of the sections of the Lk...
. Nagata's conjecture on automorphisms concerns the existence of wild automorphisms of polynomial algebras in three variables. Recent work has solved this latter problem in the affirmative.
Selected works
- Nagata, Masayoshi Local rings. Interscience Tracts in Pure and Applied Mathematics, No. 13. Interscience Publishers (a division of John Wiley & Sons), New York-London 1962, reprinted by R. E. Krieger Pub. Co, 1975. ISBN 0882752286