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Rudolf Friedrich Alfred Clebsch (19 de enero de 1833 - 7 de noviembre de 1872) fue un matemático alemán que hizo importantes contribuciones en geometría algebraica y teoría de invariantes. Estudió en la Universidad de Königsberg y comenzó su carrera docente en la Universidad Humboldt de Berlín y la Universidad de Karlsruhe.
Rudolf Friedrich Alfred Clebsch (19 January 1833 – 7 November 1872) was a German mathematician who made important contributions to algebraic geometry and invariant theory. He attended the University of Königsberg and was habilitated at Berlin. He subsequently taught in Berlin and Karlsruhe.
Alfred Clebsch was a German mathematician worked on algebraic geometry and was a co-founder of Mathematische Annalen. View two larger pictures. Biography. Alfred Clebsch's parents were Ernst Friedrich Leopold Clebsch (1802-1863) and Pauline Ramberg (died 1864).
Rudolf Friedrich Alfred Clebsch (19 de enero de 1833 - 7 de noviembre de 1872) fue un matemático alemán que hizo importantes contribuciones en geometría algebraica y teoría de invariantes.
- The Jerrard Form and C Invariant
- The Curve \
- Completion of The First Geometrical Interpretation
- Geometrical Interpretation of “The Tschirnhaus Method”
- The Diagonal Surface
- Interpretation of Kronecker’s Approach
Let us now turn to Clebsch’s research. Clebsch gave a list of invariants and covariants of the quintic, referring to works he and Gordan had done earlier (Clebsch and Gordan 1867).Footnote 47 Among them, the most important for what follows is an invariant of degree 12 that Clebsch noted C. Other invariants A, B and linear covariants \(\alpha ,\delt...
With the aim of finding a tangent to the curve \(C=0\), Clebsch extensively studied the latter and in particular determined its genus.Footnote 51 Let us recall that the genus of an algebraic curve is an integer depending on its degree and on its possible singularities. More specifically, the genus of a smooth curve of degree nis the number and in t...
This genus computation was important to Clebsch because it enabled him to deploy his past research on birational mapsFootnote 53 to successively transform the curve \(C=0\). In this process, a crucial point was the possibility of finding a birational map between the projective plane and any cubic surface, i.e., any algebraic surface defined by a po...
According to Clebsch, this geometrical interpretation of the Tschirnhaus method was “not so direct” as the previous one concerning the quadratic substitution.Footnote 61He recalled that this method consists in considering the transformation where a, b, c, d, and e should be chosen so that the coefficients of the second, third, and fourth powers in ...
In order to investigate more closely the surface defined by the equations \(\varPhi = X=0\), Clebsch changed the pentahedric coordinates. Indeed, he came back to \(\xi _1,\xi _2,\ldots ,\xi _5\), linked by the relation \(\sum \xi _i=0\), so that the equation of the cubic surface was then \(\sum \xi _i^3=0\). The planes \(\xi _i=0\) are the five fac...
As explained earlier, Kronecker had proven that the quintic can be brought into a pure equation \(z^5=A\)thanks to the multiplier equation (of degree 6) associated to the transformation of order 5 of elliptic functions. Clebsch carried out his geometrical interpretation of this approach in two steps. The first one was to find an equation of degree ...
- François Lê
- francois.le10@gmail.com
- 2017
6 de ago. de 2021 · Alfred Clebsch is widely considered to be one of the fathers of algebraic geometry. Born in Prussia in 1833, he completed his Ph.D. at just 21, and went on to publish two important...
6 de ago. de 2021 · New analysis of two recently translated papers, first published in the 1850s, assesses the early methods used by Alfred Clebsch to describe the flow of incompressible fluids, and explores their impact on active areas of cutting-edge research
