SeDiMO swMATH ID: 7826 Software Authors: Baur, Karin; Draisma, Jan; de Graaf, Willem A. Description: Secant dimensions of minimal orbits: computations and conjectures Let G be a connected reductive complex algebraic group and let V be a nontrivial irreducible module for G. It is well-known that the projective space ℙV contains a unique (Zariski)-closed orbit X consisting of the highest-weight lines and called the minimal orbit. Denote by C⊂V the affine cone over X. Moreover, denote by kX the k-th secant variety of k-secant (k-1)-planes to X, and by kC its affine cone. In the paper under review, the authors present an algorithm, called sedimo and available for download from http://www.win.tue.nl/ jdraisma/, which allow to compute dimkC. After dealing with some implementation issues, they list some conjectures about secant dimensions especially regarding Grassmannians and Segre products. Moreover, for these classes of minimal orbits, the authors give a proof of the relation between the existence of certain codes and non-defectiveness of certain higher secant varieties. Homepage: http://www.win.tue.nl/~jdraisma/index.php?location=programs Dependencies: GAP Keywords: Projective techniques; classical groups; higher secant varieties Related Software: Macaulay2; Bertini; GAP; SLA; PHCpack; Magma Cited in: 14 Publications Further Publications: http://www.win.tue.nl/~jdraisma/index.php?location=publications all top 5 Cited by 22 Authors 6 Abo, Hirotachi 4 Bernardi, Alessandra 3 Brambilla, Maria Chiara 2 Draisma, Jan 2 Mourrain, Bernard 1 Arrondo, Enrique 1 Ballico, Edoardo 1 Baur, Karin 1 Boralevi, Ada 1 Buczyński, Jarosław 1 Carlini, Enrico 1 Catalisano, Maria Virginia 1 Daleo, Noah S. 1 de Graaf, Willem Adriaan 1 Gimigliano, Alessandro 1 Hauenstein, Jonathan D. 1 Marques, Pedro Macias 1 Oneto, Alessandro 1 Ottaviani, Giorgio Maria 1 Peterson, Chris 1 Vanzo, Davide 1 Wan, Jia all top 5 Cited in 10 Serials 3 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Experimental Mathematics 2 Mathematics 1 Collectanea Mathematica 1 Journal of Pure and Applied Algebra 1 Journal of Symbolic Computation 1 Differential Geometry and its Applications 1 Linear Algebra and its Applications 1 Journal of Algebraic Geometry 1 Communications in Contemporary Mathematics all top 5 Cited in 6 Fields 14 Algebraic geometry (14-XX) 8 Linear and multilinear algebra; matrix theory (15-XX) 1 Commutative algebra (13-XX) 1 Associative rings and algebras (16-XX) 1 Convex and discrete geometry (52-XX) 1 Numerical analysis (65-XX) Citations by Year