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Prolongations and Computational Algebra

Published online by Cambridge University Press:  20 November 2018

Jessica Sidman  and
Seth Sullivant
Jessica Sidman
Affiliation:
Department of Mathematics and Statistics, Mount Holyoke College, South Hadley, MA 01075, U.S.A., e-mail: [email protected]
Seth Sullivant
Affiliation:
Department of Mathematics, North Carolina State University, Raleigh, NC, USA, e-mail: [email protected]
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Abstract

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We explore the geometric notion of prolongations in the setting of computational algebra, extending results of Landsberg and Manivel which relate prolongations to equations for secant varieties. We also develop methods for computing prolongations that are combinatorial in nature. As an application, we use prolongations to derive a new family of secant equations for the binary symmetric model in phylogenetics.

Keywords

13P1014M99
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 61 , Issue 4 , 01 August 2009 , pp. 930 - 949
Copyright
Copyright © Canadian Mathematical Society 2012

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