The lattice size of a lattice polygon
Copyright policy )The lattice size of a lattice polygon
We give upper bounds on the minimal degree of a model in $\mathbb{P}^2$ and the minimal bidegree of a model in $\mathbb{P}^1 \times \mathbb{P}^1$ of the curve defined by a given Laurent polynomial, in terms of the combinatorics of the Newton polygon of the latter. We prove in various cases that this bound is sharp as soon as the polynomial is sufficiently generic with respect to its Newton polygon.
- KU Leuven Belgium
- University of Cape Town South Africa
- Ghent University Belgium
Minimal bidegree, Newton polygon, LINEAR SERIES, minimal degree, 0101 Pure Mathematics, Computation Theory & Mathematics, Minimal degree, NUMBER, math.AG, Mathematics - Algebraic Geometry, Algebraic curve, FOS: Mathematics, Mathematics - Combinatorics, 4901 Applied mathematics, math.CO, Toric varieties, Newton polyhedra, Okounkov bodies, Algebraic Geometry (math.AG), Science & Technology, lattice width, algebraic curve, Lattice width, CURVES, minimal bidegree, Plane and space curves, Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry), Physical Sciences, 4904 Pure mathematics, Combinatorics (math.CO), Mathematics
Minimal bidegree, Newton polygon, LINEAR SERIES, minimal degree, 0101 Pure Mathematics, Computation Theory & Mathematics, Minimal degree, NUMBER, math.AG, Mathematics - Algebraic Geometry, Algebraic curve, FOS: Mathematics, Mathematics - Combinatorics, 4901 Applied mathematics, math.CO, Toric varieties, Newton polyhedra, Okounkov bodies, Algebraic Geometry (math.AG), Science & Technology, lattice width, algebraic curve, Lattice width, CURVES, minimal bidegree, Plane and space curves, Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry), Physical Sciences, 4904 Pure mathematics, Combinatorics (math.CO), Mathematics
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