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From Classical to Modern Algebraic Geometry

Part of the Trends in the History of Science Book Series

Editors: Casnati, Gianfranco; Conte, Alberto; Gatto, Letterio; Giacardi, Livia; Marchisio, Marina; Verra, Alessandro

DOI: 10.1007/978-3-319-32994-9

ISBN: 978-3-319-32992-5

Publisher: Springer International Publishing - Springer Journals

Apr 22, 2017

1 - 10 of 16 Chapters

LitStream

Segre’s University Courses and the Blossoming of the Italian School of Algebraic Geometry

Conte, Alberto; Giacardi, Livia

Pages: 3 –91

[One of the greatest architects of the “geometric Risorgimento” (Coolidge 1927, 352) in Italy, Corrado Segre provides a shining example of the role of mentor in the history of mathematics. His university courses were a veritable forge for future researchers. The years between 1891 and the...
LitStream

Corrado Segre and His Disciples: the Construction of an International Identity for the Italian School of Algebraic Geometry

Luciano, Erika; Roero, Clara Silvia

Pages: 93 –241

[It is well known that the construction of an identity for the Italian School of Algebraic Geometry directed by C. Segre was the result of a complex dynamic of scientific exchanges with the international mathematical community. In particular, Felix Klein was a reference interlocutor for Segre,...
LitStream

Segre, Klein, and the Theory of Quadratic Line Complexes

Rowe, David E.

Pages: 243 –263

[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...
LitStream

Segre and the Foundations of Geometry: From Complex Projective Geometry to Dual Numbers

Brigaglia, Aldo

Pages: 265 –288

[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...
LitStream

Segre, Castelnuovo, Enriques: Missing Links

Gario, Paola

Pages: 289 –323

[At the end of the 1880s, Segre guided Castelnuovo’s research towards the geometry of algebraic curves, introducing Castelnuovo, whose earlier studies had been focused on n-dimensional projective geometry, to birational geometry, which is the starting point of the Italian school of algebraic...
LitStream

Corrado Segre: Biographical Timeline

Giacardi, Livia

Pages: 325 –348

[Corrado is born in Saluzzo to a well-to-do Jewish family. In 1870 the family moves to Turin. His father, Abramo Segre, was an industrialist in silk production, and his mother, Estella De Benedetti, came from a cultivated family of the upper-middle class. Corrado had two brothers, Mario e Arturo.]
LitStream

Algebraic Elements of the Cremona Groups

Blanc, Jérémy

Pages: 351 –360

[This article studies algebraic elements of the Cremona group. In particular, we show that the set of all these elements is a countable union of closed subsets but it is not closed.]
LitStream

Segre Functions in Multiprojective Spaces and Tensor Analysis

Chiantini, Luca; Sacchi, Duccio

Pages: 361 –374

[We introduce the notion of Segre function sX for a variety X embedded in a product of projective spaces and determine some initial property of sX, when X is a finite subset. We show in the last section how these properties can be used to derive results on the identifiability of specific tensors.]
LitStream

Cremona Linearizations of Some Classical Varieties

Ciliberto, Ciro; Cueto, Maria Angelica; Mella, Massimiliano; Ranestad, Kristian; Zwiernik, Piotr

Pages: 375 –407

[In this paper we present an effective method for linearizing rational varieties of codimension at least two under Cremona transformations, starting from a given parametrization. Using these linearizing Cremonas, we simplify the equations of secant and tangential varieties of some classical...
LitStream

An Account of Instanton Bundles on Hyperquadrics

Costa, Laura; Miró-Roig, Rosa M.; Pons-Llopis, Joan

Pages: 409 –428

[We study instanton bundles on three-dimensional quadrics, paying special attention to the family of ’t Hooft bundles. We give explicit families of instanton bundles which are not ’t Hooft. In the last section we propose a generalization of an instanton bundle on odd dimensional hyperquadrics...

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