History
Important dates and names; the numbers below the names refer to
the numbers in the overview of the algorithm to the right.
1850, Riemann
1870, Noether | show birational equivalence of
surfaces with a pencil of curves of genus 0 to tubular surfaces. (+algorithm!)
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1870, Noether
(3) | gives algorithm for parametrizing
tubular surfaces over the complex.
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1895, Enriques | shows birational equivalence of parametrizable surfaces
to surfaces with a pencil of curves of genus 0 or Del Pezzo surfaces. (over any field, no algorithm)
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1896, Castelnuovo
(1) | gives necessary and sufficient criterion for
(rational) parametrizibility of surfaces over the complex.
(no algorithm)
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1908, Comessati
1965, Manin
(2a) | classify Del Pezzo surfaces over the reals.
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1997, Schicho
(2) | gives algorithm for rational parametrization of
algebraic surfaces in his PhD thesis, both over the reals and the
complex. (constructive version of Enriques' theorem: general case is
reduced to several known special cases)
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