Related papers: Toric Amplitudes and Universal Adjoints
Growth of the Hilbert-Poincar\"e series for the rational homology of the free loop space of a toric space is addressed. In case the toric space is a manifold, the structure of the fan dictates whether the Hilbert-Poincar\"e series has…
We provide an efficient recursive formula to compute the canonical forms of arbitrary $d$-dimensional simple polytopes, which are convex polytopes such that every vertex lies precisely on $d$ facets. For illustration purposes, we explicitly…
The amplitude for the singlet channels in the 4-point function of the fundamental field in the conformal field theory of the 2d $O(n)$ model is studied as a function of $n$. For a generic value of $n$, the 4-point function has infinitely…
Generalizing the concepts of Stanley-Reisner and affine monoid algebras, one can associate to a rational pointed fan the toric face ring. Assuming that this ring is Cohen-Macaulay, the main result of this paper is to characterize the…
The field-theoretic wavefunction has received renewed attention with the goal of better understanding observables at the boundary of de Sitter spacetime and studying the interior of Minkowski or general FLRW spacetime. Understanding the…
We describe the structure of simplicial locally convex fans associated to even-dimensional complete toric varieties with signature 0. They belong to the set of such toric varieties whose even degree Betti numbers yield a top gamma vector…
We show that the equivariant Chow cohomology ring of a toric variety is naturally isomorphic to the ring of integral piecewise polynomial functions on the associated fan. This gives a large class of singular spaces for which localization…
We introduce strong congruence spaces, which are topological spaces that provide a useful concept of dimension for monoid schemes. We study their properties and show that, given a toric monoid scheme over an algebraically closed basis, its…
We describe an explicit presentation of the ring of integral piecewise-exponential functions on a unimodular fan as a quotient of the Stanley-Reisner ring of the fan. This gives rise to a presentation of K-rings of smooth toric varieties…
We consider subtorus actions on complex toric varieties. A natural candidate for a categorical quotient of such an action is the so-called toric quotient, a universal object constructed in the toric category. We prove that if the toric…
For the example of the logarithmic triplet theory at c=-2 the chiral vacuum torus amplitudes are analysed. It is found that the space of these torus amplitudes is spanned by the characters of the irreducible representations, as well as a…
In the first part of this paper, we study the properties of some particular plurisubharmonic functions, namely the toric ones. The main result of this part is a precise description of their multiplier ideal sheaves, which generalizes the…
We present an algebraic method to study four-dimensional toric varieties by lifting matrix equations from the special linear group ${\rm SL}_2({\mathbb Z})$ to its preimage in the universal cover of ${\rm SL}_2({\mathbb R})$. With this…
Associated to a toric variety $X$ of dimension $r$ over a field $k$ is a fan $\Delta$ on $\Bbb R^r$. The fan $\Delta$ is a finite set of cones which are in one-to-one correspondence with the orbits of the torus action on $X$. The fan…
We give a necessary and sufficient condition for the nonsingular projective toric variety associated to the graph cubeahedron of a finite simple graph to be Fano or weak Fano in terms of the graph.
Let $X$ be a smooth Fano fourfold admitting a conic bundle structure. We show that $X$ is toric if and only if $X$ admits an amplified endomorphism; in this case, $X$ is a rational variety.
In this paper we study the geometry and combinatorics of the possible rational polyhedral fans with a given set of rays. The main questions we consider are when such fans are projective, complete, or simplicial. To answer these questions we…
We give a structure theorem for n-dimensional smooth toric Fano varieties whose associated polytope has "many" pairs of centrally symmetric vertices.
Hadron-nucleus amplitudes at high energies are studied in the "toy" Regge model in zero transverse dimension for finite nuclei, when the standard series of fan diagrams is converted into a finite sum and looses physical sense at quite low…
Toric orbifolds are a topological generalization of projective toric varieties associated to simplicial fans. We introduce some sufficient conditions on the combinatorial data associated to a toric orbifold to ensure the existence of an…