Criteria for strict monotonicity of the mixed volume of convex polytopes

DOI10.1515/advgeom-2018-0024zbMath1428.52011arXiv1702.07676OpenAlexW2963464815WikidataQ127597061 ScholiaQ127597061MaRDI QIDQ2334550

Ivan Soprunov, Frédéric Bihan

Publication date: 7 November 2019

Published in: Advances in Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1702.07676

zbMATH Keywords

Newton polytopemixed volumeBKK boundsparse polynomial systemBrunn-Minkowsky theory

Mathematics Subject Classification ID

Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) (52B20) Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Mixed volumes and related topics in convex geometry (52A39) Solving polynomial systems; resultants (13P15)

Related Items (6)

The Maximum Likelihood Degree of Sparse Polynomial Systems ⋮ Unmixing the mixed volume computation ⋮ Dimension results for extremal-generic polynomial systems over complete toric varieties ⋮ Mixed volume of small reaction networks ⋮ Polyhedra of small relative mixed volume ⋮ Curve valuations and mixed volumes in the implicitization of rational varieties

Uses Software

• libtropicana

Cites Work

• Unnamed Item
• Systems of equations with a single solution
• The number of roots of a system of equations
• Newton polyhedra and the genus of complete intersections
• On the Newton polytope of the resultant
• A convex geometric approach to counting the roots of a polynomial system
• The Cayley trick, lifting subdivisions and the Bohne-Dress theorem on zonotopal tilings
• Unmixing the mixed volume computation
• Bezout Inequality for Mixed Volumes
• Using Algebraic Geometry
• A Polyhedral Method for Solving Sparse Polynomial Systems
• Convex Bodies The Brunn-MinkowskiTheory

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