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

2016 | OriginalPaper | Chapter

Cremona Linearizations of Some Classical Varieties

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

Published in: From Classical to Modern Algebraic Geometry

Publisher: Springer International Publishing

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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.

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previous chapter Segre Functions in Multiprojective Spaces and Tensor Analysis
next chapter An Account of Instanton Bundles on Hyperquadrics
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Metadata
Title
Cremona Linearizations of Some Classical Varieties
Authors
Ciro Ciliberto
Maria Angelica Cueto
Massimiliano Mella
Kristian Ranestad
Piotr Zwiernik
Copyright Year
2016
Book
From Classical to Modern Algebraic Geometry

Print ISBN: 978-3-319-32992-5

Electronic ISBN: 978-3-319-32994-9

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-319-32994-9_9

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