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On the Graver complexity of codimension \(2\) matrices. (English) Zbl 1195.14067
Author’s abstract: We describe how the inherent geometric properties of the Graver bases of integer matrices of the form \(\{(1,0),(1,a),(1,b),(1,a+b)\}\) with \(a,b\in\mathbb{Z}^+\) enable us to determine that the Graver complexity of the more general matrix \({\mathcal A}=\{(1,i_1),(1,i_2),(1,i_3),(1,i_4)\}\) associated to a monomial curve in \(\mathbb{P}^3\) can be bounded as a linear relation of the entries of \({\mathcal A}\).

MSC:
14M25 Toric varieties, Newton polyhedra, Okounkov bodies
52B20 Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry)
13P99 Computational aspects and applications of commutative rings
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