Ernst Eduard Kummer (29 January 1810 – 14 May 1893) was a German mathematician. Skilled in applied mathematics, Kummer trained German army officers in ballistics; afterwards, he taught for 10 years in a gymnasium, the German equivalent of high school, where he inspired the mathematical career of Leopold Kronecker.
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👉 Ernst Kummer in the context of Leopold Kronecker
Leopold Kronecker (German: [ˈkʁoːnɛkɐ]; 7 December 1823 – 29 December 1891) was a German mathematician who worked on number theory, abstract algebra and logic, and criticized Georg Cantor's work on set theory. Heinrich Weber quoted Kroneckeras having said, "Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk" ("God made the integers, all else is the work of man").Kronecker was a student and life-long friend of Ernst Kummer.
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- ⭐ Core Definition: Ernst Kummer
- 👉 Ernst Kummer in the context of Leopold Kronecker
- Ernst Kummer in the context of Kummer surface
Ernst Kummer in the context of Kummer surface
In algebraic geometry, a Kummer quartic surface, first studied by Ernst Kummer (1864), is an irreducible nodal surface of degree 4 in with the maximal possible number of 16 double points. Any such surface is the Kummer variety of the Jacobian variety of a smooth hyperelliptic curve of genus 2; i.e. a quotient of the Jacobian by the Kummer involution x ↦ −x. The Kummer involution has 16 fixed points: the 16 2-torsion point of the Jacobian, and they are the 16 singular points of the quartic surface. Resolving the 16 double points of the quotient of a (possibly nonalgebraic) torus by the Kummer involution gives a K3 surface with 16 disjoint rational curves; these K3 surfaces are also sometimes called Kummer surfaces.
Other surfaces closely related to Kummer surfaces include Weddle surfaces, wave surfaces, and tetrahedroids.
View the full Wikipedia page for Kummer surface