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RESEARCH PRODUCT

Segre, Klein, and the Theory of Quadratic Line Complexes

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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.