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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
##### Keywords:
Graver complexity; Hilbert bases; monomial curves
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