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From Classical to Modern Algebraic GeometryCremona Linearizations of Some Classical Varieties

From Classical to Modern Algebraic Geometry: Cremona Linearizations of Some Classical Varieties [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 examples, including Veronese, Segre and Grassmann varieties. We end the paper by treating the special case of the Segre embedding of the n-fold product of projective spaces, where cumulant Cremonas, arising from algebraic statistics, appear as specific cases of our general construction.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

From Classical to Modern Algebraic GeometryCremona Linearizations of Some Classical Varieties

Part of the Trends in the History of Science Book Series
Editors: Casnati, Gianfranco; Conte, Alberto; Gatto, Letterio; Giacardi, Livia; Marchisio, Marina; Verra, Alessandro
Ciliberto, Ciro; Cueto, Maria Angelica; Mella, Massimiliano; Ranestad, Kristian; Zwiernik, Piotr
From Classical to Modern Algebraic Geometry — Apr 22, 2017
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References (23)

Publisher
Springer International Publishing
Copyright
© Springer International Publishing Switzerland 2016
ISBN
978-3-319-32992-5
Pages
375 –407
DOI
10.1007/978-3-319-32994-9_9
Publisher site
See Chapter on Publisher Site

Abstract

[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 examples, including Veronese, Segre and Grassmann varieties. We end the paper by treating the special case of the Segre embedding of the n-fold product of projective spaces, where cumulant Cremonas, arising from algebraic statistics, appear as specific cases of our general construction.]

Published: Apr 22, 2017

Keywords: Cremona transformations; Birational maps; Segre and Veronese varieties; Cumulants; Secant cumulants; Primary 14E25; Secondary 14E08; 14N05; 14E05

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