Related papers: Hilbert's 14th Problem and Cox Rings

In this paper, we show that incoherent Hilbert Eisenstein series for a real quadratic fields can be expressed as the Doi-Naganums lift of an incoherent Eisenstein series over $\mathbb{Q}$. As an application, we show when $N$ is odd and…

A general theory of vector-valued modular functions, holomorphic in the upper half-plane, is presented for finite dimensional representations of the modular group. This also provides a description of vector-valued modular forms of arbitrary…

This paper deals with the problem of computing a generating set for the Cox ring $R(X)$ of a smooth projective rational surface $X$ with nef anticanonical class. In case $R(X)$ is finitely generated, we show that the degrees of its…

For a positive proportion of primes $p$ and $q$, we prove that $\mathbb{Z}$ is Diophantine in the ring of integers of $\mathbb{Q}(\sqrt[3]{p},\sqrt{-q})$. This provides a new and explicit infinite family of number fields $K$ such that…

We construct an example of blow-up in a flow of min-plus linear operators arising as solution operators for a Hamilton-Jacobi equation with a Hamiltonian of the form |p|^alpha+U(x,t), where alpha>1 and the potential U(x,t) is uniformly…

A comprehensive review of the discrete quantum mechanics with the pure imaginary shifts and the real shifts is presented in parallel with the corresponding results in the ordinary quantum mechanics. The main subjects to be covered are the…

We study quadratic algebras over a field $\textbf{k}$. We show that an $n$-generated PBW algebra $A$ has finite global dimension and polynomial growth \emph{iff} its Hilbert series is $H_A(z)= 1 /(1-z)^n$. Surprising amount can be said when…

Here we investigate meaningful families of vector bundles on a very general polarized $K3$ surface $(X,H)$ and on the corresponding Hyper--Kaehler variety given by the Hilbert scheme of points $X^{[k]}:= {\rm Hilb}^k(X)$, for any integer $k…

Let $S$ be the affine plane regarded as a toric variety with an action of the 2-dimensional torus $T$. We study the equivariant Chow ring $A_{K}^*(Hilb^n(S))$ of the punctual Hilbert scheme $Hilb^n(S)$ with equivariant coefficients…

We introduce a systematic framework for counting and finding independent operators in effective field theories, taking into account the redundancies associated with use of the classical equations of motion and integration by parts. By…

In recent years, digraph induced generators of quantum dynamical semigroups have been introduced and studied, particularly in the context of unique relaxation and invariance. In this article we define the class of pair block diagonal…

For a recollement of derived module categories of rings, we provide sufficient conditions to guarantee the additivity formula of higher algebraic K-groups of the rings involved, and establish a long Mayer-Vietoris exact sequence of higher…

In this paper we analyze the Hilbert boundary-value problem of the theory of analytic functions for an $(N+1)$-connected circular domain. An exact series-form solution has already been derived for the case of continuous coefficients.…

We investigate the standard graded $k$-algebras over a field $k$ of characteristic zero for which general linear forms are exact zero divisors. We formulate a conjecture regarding the Hilbert function of such rings. We prove our conjecture…

This paper explores a full generalization of the classical corner-vector method for constructing weighted spherical designs, which we call the {\it generalized corner-vector method}. First we establish a uniform upper bound for the degree…

We use the rational tableaux introduced by Stembridge to give a bideterminant basis for a normal reductive monoid and for its variety of noninvertible elements. We also obtain a bideterminant basis for the full coordinate ring of the…

Let $X=X_1\cup \cdots \cup X_s\subset \mathbb {P}^n$, $n\ge 4$, be a general union of smooth non-special curves with $X_i$ of degree $d_i$ and genus $g_i$ and $d_i\ge \max \{2g_i-1,g_i+n\}$ if $g_i>0$. We prove that $X$ has maximal rank,…

We consider Blanchet, Habegger, Masbaum and Vogel's universal construction of topological theories in dimension two, using it to produce interesting theories that do not satisfy the usual two-dimensional TQFT axioms. Kronecker's…

Given an action of a compact group on a complex vector bundle, there is an induced action of the group on the associated Cuntz-Pimsner algebra. We determine conditions under which this action has finite Rokhlin dimension.

Let $\omega$ be a Kahler form on $M$, which is a torus $T^4$, a $K3$ surface or an Enriques surface, let $M\#n\overline{\mathbb{CP}^2}$ be $n-$point Kahler blowup of $M$. Suppose that $\kappa=[\omega]$ satisfies certain irrationality…