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Lovász–Saks–Schrijver
ideals and coordinate sections of determinantal varieties
Aldo Conca and Volkmar Welker |
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Vol. 13 (2019), No. 2, 455–484
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Abstract |
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Motivated by questions in algebra and combinatorics we study two ideals associated to a simple graph :
In characteristic these two ideals turn out to be closely related and algebraic properties such as being radical, prime or a complete intersection transfer from the Lovász–Saks–Schrijver ideal to the determinantal ideal. For Lovász–Saks–Schrijver ideals we link these properties to combinatorial properties of and show that they always hold for large enough. For specific classes of graphs, such a forests, we can give a complete picture and classify the radical, prime and complete intersection Lovász–Saks–Schrijver ideals. |
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Keywords
determinantal rings, complete intersections, ideals
associated to graphs, Gröbner bases.
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Mathematical Subject Classification 2010
Primary: 05E40
Secondary: 05C62, 13P10
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Milestones
Received: 8 February 2018
Revised: 3 November 2018
Accepted: 24 December 2018
Published: 2 March 2019
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Authors |
| Aldo Conca | |
| Dipartimento di Matematica Università di Genova 16146 Genova Italy |
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| Volkmar Welker | |
| Fachbereich Mathematik und
Informatik Philipps-Universität Marburg 35032 Marburg Germany |
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