George Rushing Kempf (

Globe, Arizona Globe ( apw, Bésh Baa Gowąh "Place of Metal") is a city in Gila County, Arizona, United States. As of the 2020 census, the population of the city was 7,249. The city is the county seat of Gila County. Globe was founded c. 1875 as a mining cam ...

, August 12, 1944 –

Lawrence, Kansas Lawrence is the county seat of Douglas County, Kansas, Douglas County, Kansas, United States, and the sixth-largest city in the state. It is in the northeastern sector of the state, astride Interstate 70, between the Kansas River, Kansas and Waka ...

, July 16, 2002) was a mathematician who worked on

algebraic geometry Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical ...

, who proved the Riemann–Kempf singularity theorem, the

Kempf–Ness theorem In algebraic geometry, the Kempf–Ness theorem, introduced by , gives a criterion for the stability of a vector in a representation of a complex reductive group. If the complex vector space is given a norm that is invariant under a maximal comp ...

, the

Kempf vanishing theorem In algebraic geometry, the Kempf vanishing theorem, introduced by , states that the higher cohomology group ''H'i''(''G''/''B'',''L''(λ)) (''i'' > 0) vanishes whenever λ is a dominant weight of ''B''. Here ''G'' is a reductive a ...

, and who introduced Kempf varieties.

Mumford on Kempf

'I met George in 1970 when he burst on the algebraic geometry scene with a spectacular PhD thesis. His thesis gave a wonderful analysis of the singularities of the subvarieties

W_r

of the Jacobian of a curve obtained by adding the curve to itself

r

times inside its Jacobian. This was one of the major themes that he pursued throughout his career: understanding the interaction of a curve with its Jacobian and especially to the map from the

r

-fold symmetric product of the curve to the Jacobian. In his thesis he gave a determinantal representation both of

W_r

and of its tangent cone at all its singular points, which gives you a complete understanding of the nature of these singularities' –

David Mumford David Bryant Mumford (born 11 June 1937) is an American mathematician known for his work in algebraic geometry and then for research into vision and pattern theory. He won the Fields Medal and was a MacArthur Fellow. In 2010 he was awarded t ...

'One of the things that distinguished his work was the total mastery with which he used higher cohomology. A paper which, I believe, every new student of algebraic geometry should read, is his elementary proof of the Riemann-Roch theorem on curves: “Algebraic Curves” in Crelle, 1977. That such an old result could be treated with new insight was the work of a master.' – David Mumford

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External links

George Rushing Kempf
{{DEFAULTSORT:Kempf, George 1944 births 2002 deaths 20th-century American mathematicians 21st-century American mathematicians Algebraic geometers Johns Hopkins University alumni University of Illinois Urbana-Champaign alumni Columbia University alumni Johns Hopkins University faculty People from Lawrence, Kansas People from Baltimore People from Globe, Arizona Mathematicians from Arizona