Related papers: On the integral Caratheodory property

A complex manifold $X$ is called "LCK manifolds with potential" if it can be realized as a complex submanifold of a Hopf manifold. Let $Y$ its $\Z$-covering, considered as a complex submanifold in $C^n \backslash 0$. We prove that $Y$ is…

We study topology, particularly compactness, as an extension of Shulman's work on constructive mathematics via affine logic, while allowing propositional impredicativity. We introduce a notion of compactness in affine logic and prove the…

In this note, we work out a simple inductive proof showing that every polyhedral cone K is the conic hull of a finite set X of vectors. The base cases of the induction are linear subspaces and linear halfspaces of linear subspaces. The…

Due to a result by Gallot a Riemannian cone over a complete Riemannian manifold is either flat or has an irreducible holonomy representation. This is false in general for indefinite cones but the structures induced on the cone by holonomy…

We investigate the semigroup of integer points inside a convex cone. We extend classical results in integer linear programming to integer conic programming. We show that the semigroup associated with nonpolyhedral cones can sometimes have a…

A strong quantitative form of Manin's conjecture is established for a certain variety in biprojective space. The singular integral in an application of the circle method involves the third power of the integral sine function, and is…

We construct a finitely presented group with infinitely many non-homeomorphic asymptotic cones. We also show that the existence of cut points in asymptotic cones of finitely presented groups does, in general, depend on the choice of scaling…

A finitely generated module $M$ over a commutative Noetherian ring $R$ is called an $I$-Cohen Macaulay module, if \[ \grade(I,M) + \dim(M/IM)= \dim(M), \] where $I$ is a proper ideal of $R$. The aim of this paper is to study the structure…

Let k be an algebraically closed field of characteristic zero. We show that the centre of a homologically homogeneous, finitely generated k-algebra has rational singularities. In particular if a finitely generated normal commutative…

We investigate structural properties of the completely positive semidefinite cone $\mathcal{CS}_+^n$, consisting of all the $n \times n$ symmetric matrices that admit a Gram representation by positive semidefinite matrices of any size. This…

The study of the cone of submodular functions goes back to Jack Edmonds' seminal 1970 paper, which already highlighted the difficulty of characterizing its extreme rays. Since then, researchers from diverse fields have sought to…

We introduce the notion of a chopped and sliced cone in combinatorial geometry and prove two structure theorems for the number of integral points in the individual slices of such a cone. We observe that this notion applies to weight…

We expand the notion of characteristic formula to infinite finitely presentable subdirectly irreducible algebras. We prove that there is a continuum of varieties of Heyting algebras containing infinite finitely presentable subdirectly…

Does a space enjoying good finiteness properties admit an algebraic model with commensurable finiteness properties? In this note, we provide a rational homotopy obstruction for this to happen. As an application, we show that the maximal…

Let $X$ be a cubic fourfold in $P^5_{C}$. We prove that, assuming the Hodge conjecture for the product $S \times S$, where $S$ is a complex surface, and the finite dimensionality of the Chow motive $h(S)$, there are at most a countable…

In the finite-dimensional case, we present a new approach to the theory of cones with a mapping cone symmetry, first introduced by St{\o}rmer. Our method is based on a definition of an inner product in the space of linear maps between two…

A special class of orthogonal rational functions (ORFs) is presented in this paper. Starting with a sequence of ORFs and the corresponding rational functions of the second kind, we define a new sequence as a linear combination of the…

We generalize Voronoi's theory of perfect quadratic forms to generalized copositive matrices over a closed convex and full-dimensional cone K. We introduce a notion of a K-copositive minimum and of perfect K-copositive matrices. We consider…

We give a canonical construction of a balanced big Cohen-Macaulay algebra for a domain of finite type over $\mathbb C$ by taking ultraproducts of absolute integral closures in positive characteristic. This yields a new tight closure…

Let P be a d-dimensional lattice polytope. We show that there exists a natural number c_d, only depending on d, such that the multiples cP have a unimodular cover for every natural number c >= c_d. Actually, a subexponential upper bound for…