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From Classical to Modern Algebraic GeometrySegre and the Foundations of Geometry: From Complex Projective Geometry to Dual Numbers

From Classical to Modern Algebraic Geometry: Segre and the Foundations of Geometry: From Complex... [In 1886 Corrado Segre wrote to Felix Klein about his intention to study ‘géométrie projective pure’, completing and developing the work of von Staudt. He would continue this research project throughout the whole of his scientific life. In 1889, following a suggestion of Segre, Mario Pieri published his translation of the Geometrie der Lage, and from 1889 to 1890 Segre published four important papers, “Un nuovo campo di ricerche geometriche”, in which he completely developed complex projective geometry, considering new mathematical objects such as antiprojectivities and studying the Hermitian forms from a geometrical point of view with the related ‘hyperalgebraic varieties’. Segre developed the same ideas in 1892 in a new paper published in the Matematische Annalen, in which he also considers the so-called “bicomplex numbers” and provided the first example of a projective geometry on an algebra with zero-divisors. In 1891, during one of his celebrated courses in higher geometry, Segre asked his students to find a system of independent axioms for projective hyperspatial geometry. Fano, Enriques, Pieri and Amodeo, who wrote important papers, followed this proposal.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

From Classical to Modern Algebraic GeometrySegre and the Foundations of Geometry: From Complex Projective Geometry to Dual Numbers

Part of the Trends in the History of Science Book Series
Editors: Casnati, Gianfranco; Conte, Alberto; Gatto, Letterio; Giacardi, Livia; Marchisio, Marina; Verra, Alessandro
Brigaglia, Aldo
From Classical to Modern Algebraic Geometry — Apr 22, 2017
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References (28)

Publisher
Springer International Publishing
Copyright
© Springer International Publishing Switzerland 2016
ISBN
978-3-319-32992-5
Pages
265 –288
DOI
10.1007/978-3-319-32994-9_4
Publisher site
See Chapter on Publisher Site

Abstract

[In 1886 Corrado Segre wrote to Felix Klein about his intention to study ‘géométrie projective pure’, completing and developing the work of von Staudt. He would continue this research project throughout the whole of his scientific life. In 1889, following a suggestion of Segre, Mario Pieri published his translation of the Geometrie der Lage, and from 1889 to 1890 Segre published four important papers, “Un nuovo campo di ricerche geometriche”, in which he completely developed complex projective geometry, considering new mathematical objects such as antiprojectivities and studying the Hermitian forms from a geometrical point of view with the related ‘hyperalgebraic varieties’. Segre developed the same ideas in 1892 in a new paper published in the Matematische Annalen, in which he also considers the so-called “bicomplex numbers” and provided the first example of a projective geometry on an algebra with zero-divisors. In 1891, during one of his celebrated courses in higher geometry, Segre asked his students to find a system of independent axioms for projective hyperspatial geometry. Fano, Enriques, Pieri and Amodeo, who wrote important papers, followed this proposal.]

Published: Apr 22, 2017

Keywords: Projective Geometry; Hermitian Form; Geometric Entity; Dual Number; Bicomplex Number

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