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From Classical to Modern Algebraic GeometrySegre, Klein, and the Theory of Quadratic Line Complexes

From Classical to Modern Algebraic Geometry: Segre, Klein, and the Theory of Quadratic Line... [Two of C. Segre’s earliest papers, (Segre 1883a) and (Segre 1884), dealt with the classification of quadratic line complexes, a central topic in line geometry. These papers, the first written together with Gino Loria, were submitted to Felix Klein in 1883 for publication in Mathematische Annalen. Together with the two lengthier works that comprise Segre’s dissertation, (Segre 1883b) and (Segre 1883c), they took up and completed a topic that Klein had worked on a decade earlier (when he was known primarily as an expert on line geometry). Using similar ideas, but a new and freer approach to higher-dimensional geometry, Segre not only refined and widened this earlier work but also gave it a new direction. Line geometry, as well described by Alessandro Terracini in his obituary for his mentor, proved to be an excellent starting point for both Segre and Italian algebraic geometry. The present account begins by looking back at the early work of Klein and Adolf Weiler on quadratic complexes in order to show how Segre’s two papers for Klein’s journal represented a new start that reawakened interest in a topic that had been dormant for nearly a decade. ] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

From Classical to Modern Algebraic GeometrySegre, Klein, and the Theory of Quadratic Line Complexes

Part of the Trends in the History of Science Book Series
Editors: Casnati, Gianfranco; Conte, Alberto; Gatto, Letterio; Giacardi, Livia; Marchisio, Marina; Verra, Alessandro
Rowe, David E.
From Classical to Modern Algebraic Geometry — Apr 22, 2017
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References (17)

Publisher
Springer International Publishing
Copyright
© Springer International Publishing Switzerland 2016
ISBN
978-3-319-32992-5
Pages
243 –263
DOI
10.1007/978-3-319-32994-9_3
Publisher site
See Chapter on Publisher Site

Abstract

[Two of C. Segre’s earliest papers, (Segre 1883a) and (Segre 1884), dealt with the classification of quadratic line complexes, a central topic in line geometry. These papers, the first written together with Gino Loria, were submitted to Felix Klein in 1883 for publication in Mathematische Annalen. Together with the two lengthier works that comprise Segre’s dissertation, (Segre 1883b) and (Segre 1883c), they took up and completed a topic that Klein had worked on a decade earlier (when he was known primarily as an expert on line geometry). Using similar ideas, but a new and freer approach to higher-dimensional geometry, Segre not only refined and widened this earlier work but also gave it a new direction. Line geometry, as well described by Alessandro Terracini in his obituary for his mentor, proved to be an excellent starting point for both Segre and Italian algebraic geometry. The present account begins by looking back at the early work of Klein and Adolf Weiler on quadratic complexes in order to show how Segre’s two papers for Klein’s journal represented a new start that reawakened interest in a topic that had been dormant for nearly a decade. ]

Published: Apr 22, 2017

Keywords: Singularity Surface; Linear Complex; Line Complex; Double Line; Quadric Surface

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