Geodesic
Explicit deformation of lattice ideals via chip-firing games on directed graphs
Journal of Algebraic Combinatorics, Tome 42 (2015) no. 4, pp. 1097-1110.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

For a finite index sublattice $L$ of the root lattice of type $A$, we construct a deterministic algorithm to deform the lattice ideal $I_{\mathrm{L}}$ to a nearby generic lattice ideal, answering a question posed by E. Miller and B. Sturmfels [Combinatorial commutative algebra. New York, NY: Springer (2005; Zbl 1066.13001)]. Our algorithm is based on recent results of D. Perkinson et al. [Contemp. Math. 605, 211--256 (2013; Zbl 1320.05060)] concerning commutative algebraic aspects of chip-firing on directed graphs. As an application of our deformation algorithm, we construct a cellular resolution of the lattice ideal $I_{\mathrm{L}}$ by degenerating the Scarf complex of its deformation.
Classification : 05C57, 05C20, 06B99
Keywords: lattice ideals, binomial ideals, chip-firing on graphs, directed graphs, Laplacian matrix, Scarf complex, free resolutions of ideals, explicit deformation 
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     title = {Explicit deformation of lattice ideals via chip-firing games on directed graphs},
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Backman, Spencer; Manjunath, Madhusudan. Explicit deformation of lattice ideals via chip-firing games on directed graphs. Journal of Algebraic Combinatorics, Tome 42 (2015) no. 4, pp. 1097-1110. http://geodesic.mathdoc.fr/item/JAC_2015__42_4_a2/