Related papers: Uniform rational polytopes for Iitaka dimensions
Unimodular theory incorporating the Kaluza-Klein construction in five dimensions leads, after reduction to four dimensions, to a new class of scalar-tensor theory. The vacuum cosmological solutions display a bouncing, non singular behavior.…
We consider the class univalent log-harmonic mappings on the unit disk. Firstly, we obtain necessary and sufficient conditions for a complex-valued continuous function to be starlike or convex in the unit disk. Then we present a general…
We verify the Morrison--Kawamata conjecture for a certain class of rational threefolds, namely blowups of P^3 in the base locus of a net of quadrics with no reducible members. This seems to be the first verified case of the conjecture for…
An extension of dimensional regularization to the case of compact dimensions is presented. The procedure preserves the Kaluza-Klein tower structure, but has a regulator specific to the compact dimension. Possible 5 and 4 dimensional…
A d.c. (delta-convex) function on a normed linear space is a function representable as a difference of two continuous convex functions. We show that an infinite dimensional analogue of Hartman's theorem on stability of d.c. functions under…
Kalai's $3^d$ conjecture states that every centrally-symmetric $d$-polytope has at least $3^d$ faces. We give short proofs for two special cases: if $P$ is unconditional (that is, invariant w.r.t. reflection in any coordinate hyperplane),…
We study a relation between brick $n$-tuples of subspaces of a finite dimensional linear space, and irreducible $n$-tuples of subspaces of a finite dimensional Hilbert (unitary) space such that a linear combination, with positive…
The dominant rational maps of finite degree from a fixed variety to varieties of general type, up to birational isomorphisms, form a finite set. This has been known as the Iitaka-Severi conjecture, and is nowdays an established result, in…
We use non-perturbative U-duality symmetries of type II strings to construct new vacuum solutions. In some ways this generalizes the F-theory vacuum constructions. We find the possibilities of new vacuum constructions are very limited.…
In this paper we study the asymptotic behavior of the regularity of symbolic powers of ideals of points in a weighted projective plane. By a result of Cutkosky, Ein and Lazarsfeld, regularity of such powers behaves asymptotically like a…
Isotopic pairs and their representations are considered in a general framework of the vector superalgebra. Numerous examples of finite-dimensional and infinite-dimensional isotopic pairs are discussed. Several types of their representations…
We introduce a special class of convex rational polyhedral cones which allows to construct generalized Calabi-Yau varieties of dimension $(d + 2(r-1))$, where $r$ is a positive integer and d is the dimension of critical string vacua with…
We investigate the sets of uniform limits $A(\bar{B}_n)$, $A(\bar{D}^I)$ of polynomials on the closed unit ball $\bar{B}_n$ of $\mathbb{C}^n$ and on the cartesian product $\bar{D}^I$ where $I$ is an arbitrary set and $\bar{D}$ is the closed…
We give a classification of unitary representations of certain Polish, not necessarily locally compact, groups: the groups of all measurable functions with values in the circle and the groups of all continuous functions on compact, second…
We make a further step in the unisolvence open problem for unsymmetric Kansa collocation, proving nonsingularity of Kansa matrices with polyharmonic splines and random fictitious centers, for second-order elliptic equations with mixed…
To seek for the useful numerical analogues to the Iitaka dimension, various numerical Iitaka dimensions have been defined from a number of different perspectives. It has been accepted that all the known numerical Iitaka dimensions coincide…
We show that the moduli spaces of bounded global $\mathcal{G}$-Shtukas with pairwise colliding legs admit $p$-adic uniformization isomorphisms by Rapoport-Zink spaces. Here $\mathcal{G}$ is a smooth affine group scheme with connected fibers…
By correcting an example by Polyanskii, we show that there exist reduced polytopes in three-dimensional Euclidean space. This partially answers the question posed by Lassak on the existence of reduced polytopes in $d$-dimensional Euclidean…
Given a fibration over a perfect field of positive characteristic, we study an Iitaka-type inequality for the anticanonical divisors. We conclude that it holds when the source of the fibration is a threefold or when the target is a curve,…
For any admissible pair of irreducible reduced crystallographic root systems, we present discrete orthogonality relations for a finite-dimensional system of Macdonald polynomials with parameters on the unit circle subject to a truncation…