Algebraic Structures on Polytopes

Algebraic Structures on Hyperkähler Manifolds Algebraic Structures on Hyperkähler Manifolds

Let M be a compact hyperkähler manifold. The hy-perkähler structure equips M with a set R of complex structures parametrized by CP 1 , called the set of induced complex structures. It was known previously that induced complex structures are non-algebraic, except may be a countable set. We prove that a countable set of induced complex structures is algebraic, and this set is dense in R. A more g...

Algebraic shifting of cyclic polytopes and stacked polytopes

Gil Kalai introduced the shifting-theoretic upper bound relation to characterize the f -vectors of Gorenstein* complexes (or homology spheres) by using algebraic shifting. In the present paper, we study the shifting-theoretic upper bound relation. First, we will study the relation between exterior algebraic shifting and combinatorial shifting. Second, by using the relation above, we will prove ...

Discriminant Polytopes, Chow Polytopes, and K-energy Asymptotics on Algebraic Curves

LetX ↪→ P be a smooth, linearly normal algebraic curve. We show that the asymptotics of the Mabuchi energy are completely determined by the discriminant polytope and the Chow polytope of X . From this we deduce a new and entirely algebraic proof that the Mabuchi energy of the rational normal curve of degree d ≥ 2 is bounded below along all degenerations. We conclude that the Moser-Trudinger-Ono...

Conference on Ordered Algebraic Structures

For n a positive integer, Ln is the variety of `-groups satisfying the equation [x, y] = e. Many of the well known but striking features of the Ln varieties carry over to varieties satisfying the laws [x, y, z] = e and [x, y, y] = e, such as the structure of finitely generated subdirectly irreducible `-groups and the respective intersections with the representable variety. Some interesting exam...

On Presentations of Algebraic Structures