Related papers: Hilbert schemes for quantum planes are projective
It is shown that a Hilbert space can be constructed for a quantum system starting from a framework in which histories are fundamental. The Decoherence Functional provides the inner product on this "History Hilbert space". It is also shown…
We show that the curvature of a positive relative line module over quantum projective space is given by $q$-integer deformation of its classical curvature. This generalises a result of Majid for the Podle\'s sphere.
The aim of this short note is to prove the formula of the Hilbert series of the preprojective algebras in arbitrary characteristic by making effective use of the formulas of the Hilbert series of differential graded (dg) algebras with Adams…
A theorem of G\"ottsche establishes a connection between cohomological invariants of a complex projective surface $S$ and corresponding invariants of the Hilbert scheme of $n$ points on $S.$ This relationship is encoded in certain infinite…
We calculate the Hochschild dimension of quantum hyperplanes using the twisted Hochschild homology.
In this paper, we will investigate the jet schemes of determinantal varieties. It is quite often the case that the geometric information concerning the jet schemes of an algebraic variety can be described, but the more refined algebraic…
In this paper we prove that the generating series of the Poincare polynomials of quasihomogeneous Hilbert schemes of points in the plane has a beautiful decomposition into an infinite product. We also compute the generating series of the…
We show that a Kirchberg algebra is semiprojective if and only if it is KK-semiprojective. In particular, this shows that a Kirchberg algebra in the UCT-class is semiprojective if and only if its K-theory is finitely generated, thereby…
Using vertex algebra techniques, we determine a set of generators for the cohomology ring of the Hilbert schemes of points on an arbitrary smooth projective surface over the field of complex numbers.
We prove a version of Manin's conjecture for the projective plane blown up in three collinear points, the base field being a global field of positive characteristic.
We define holomorphic structures on canonical line bundles of the quantum projective space $\qp^{\ell}_q$ and identify their space of holomorphic sections. This determines the quantum homogeneous coordinate ring of the quantum projective…
Various equivariant intersection numbers on Hilbert schemes of points on the affine plane are computed, some of which are organized into tau-functions of 2-Toda hierarchies. A correspondence between the equivariant intersection on Hilbert…
Given a smooth projective variety $X$ over an algebraically closed field $k$, we compute the Chow ring of the Hilbert scheme of three points on $X$, $\operatorname{Hilb}^3(X)$, as an algebra with generators and relations over the Chow ring…
We use the fact that some linear Hamiltonian systems can be considered as ``finite level'' quantum systems, and the description of quantum mechanics in terms of probabilities, to associate probability distributions with this particular…
Let $\mathcal{I}_{d,g,r}$ be the union of irreducible components of the Hilbert scheme whose general points correspond to smooth irreducible non-degenerate curves of degree $d$ and genus $g$ in $\mathbb{P}^r$. We use families of curves on…
We present a multi-image quantum encryption/decryption scheme based on blocks of bit planes and images. We provide a quantum circuit for the quantum baker map.
Quantum computing is a promising approach to harnessing strong correlation in molecular systems; however, current devices only allow for hybrid quantum-classical algorithms with a shallow circuit depth, such as the variational quantum…
We construct projective moduli spaces for torsion-free sheaves on noncommutative projective planes. These moduli spaces vary smoothly in the parameters describing the noncommutative plane and have good properties analogous to those of…
The goal of this paper is to construct the Hilbert scheme of complete intersections in the biprojective space $X=\mathbb{P}^m\times\mathbb{P}^n$ and for this, we define a partial order on the bidegrees of the bihomogeneous forms. As a…
We generalize categories of spatial partitions in the sense of C\'ebron-Weber by introducing new base partitions. This allows us to construct additional examples of free orthogonal quantum groups but yields the same class of spatial…