Computations and equations for Segre-Grassmann hypersurfaces
| Autor: | Jonathan D. Hauenstein, Luke Oeding, Noah S. Daleo |
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| Rok vydání: | 2016 |
| Předmět: |
Polynomial
Pure mathematics General Mathematics 010102 general mathematics 010103 numerical & computational mathematics 01 natural sciences Representation theory Ambient space Mathematics - Algebraic Geometry Mathematics::Algebraic Geometry Hypersurface Secant variety Mathematics Subject Classification FOS: Mathematics 0101 mathematics Variety (universal algebra) Representation (mathematics) Algebraic Geometry (math.AG) Mathematics |
| Zdroj: | Portugaliae Mathematica. 73:71-90 |
| ISSN: | 0032-5155 |
| Popis: | In 2013, Abo and Wan studied the analogue of Waring's problem for systems of skew-symmetric forms and identified several defective systems. Of particular interest is when a certain secant variety of a Segre-Grassmann variety is expected to fill the natural ambient space, but is actually a hypersurface. Algorithms implemented in Bertini are used to determine the degrees of several of these hypersurfaces, and representation-theoretic descriptions of their equations are given. We answer Problem 6.5 [Abo-Wan2013], and confirm their speculation that each member of an infinite family of hypersurfaces is minimally defined by a (known) determinantal equation. While led by numerical evidence, we provide non-numerical proofs for all of our results. Comment: 14 pages, revised content. Accepted, Portugaliae Mathematica, 2015. Updated references |
| Databáze: | OpenAIRE |
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