Convex normality of rational polytopes with long edges

DOI10.1016/j.aim.2011.12.003zbMath1251.52008arXiv0912.1068OpenAlexW2963705079MaRDI QIDQ411736

Joseph Gubeladze

Publication date: 30 April 2012

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

Full work available at URL: https://arxiv.org/abs/0912.1068

zbMATH Keywords

convex polytoperational polytopelattice polytopenormal polytopeintegrally closed polytope

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) Lattices and convex bodies (number-theoretic aspects) (11H06) Combinatorial aspects of commutative algebra (05E40) Arithmetic rings and other special commutative rings (13F99)

Related Items

Amoebas, nonnegative polynomials and sums of squares supported on circuits, Quantum jumps of normal polytopes, Unimodality questions for integrally closed lattice polytopes, Polytopal affine semigroups with holes deep inside, Sums of sets of lattice points and unimodular coverings of polytopes, Normal polytopes: between discrete, continuous, and random, Integer decomposition property of polytopes, Generalized flatness constants, spanning lattice polytopes, and the Gromov width, Cayley Sums and Minkowski Sums of Lattice Polytopes, Ehrhart series, unimodality, and integrally closed reflexive polytopes, NORMAL CYCLIC POLYTOPES AND CYCLIC POLYTOPES THAT ARE NOT VERY AMPLE, Existence of unimodular triangulations — positive results, Ehrhart series of polytopes related to symmetric doubly-stochastic matrices, Finitely many smooth \(d\)-polytopes with \(n\) lattice points

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Toroidal embeddings. I
• Mini-workshop: Projective normality of smooth toric varieties. Abstracts from the mini-workshop held August 12--18, 2007.
• An integer analogue of Carathéodory's theorem
• On the ampleness of invertible sheaves in complete projective toric varieties
• Unimodular triangulations and coverings of configurations arising from root systems
• On the Charney-Davis and Neggers-Stanley conjectures
• Unimodular covers of multiples of polytopes
• On primitive subdivisions of an elementary tetrahedron.
• On the maximal width of empty lattice simplices
• A generalization of a theorem of White
• Gröbner bases associated with positive roots and Catalan numbers
• Cyclotomic polytopes and growth series of cyclotomic lattices
• Lattice polytopes cut out by root systems and the Koszul property
• On empty lattice simplices in dimension 4
• Polytopes, Rings, and K-Theory
• Normality and covering properties of affine semigroups
• A counterexample to an integer analogue of Carathéodory's theorem
• Lectures on Polytopes
• On the Integral Carathéodory Property