Related papers: Multigraded Cayley-Chow forms
A subvariety of a complex projective space has a well-known dual variety, which is the set of its tangent hyperplanes. The purpose of this paper is to generalise this notion for a subvariety of a quite general partial flag variety. A…
New features are described for models with multi-particle area-dependent potentials, in any number of dimensions. The corresponding many-body field theories are investigated for classical configurations. Some explicit solutions are given,…
We construct in a unifying way skew-multicategories and multicategories of double and Gray-categories that we call Gray (skew) multicategories. We study their different versions depending on the types of functors and higher transforms. We…
We introduce the notion of crystallographic T-duality, inspired by the appearance of $K$-theory with graded equivariant twists in the study of topological crystalline materials. Besides giving a range of new topological T-dualities, it also…
We establish a conjecture of Mumford characterizing rationally connected complex projective manifolds in several cases.
Variations on the notions of Reedy model structures and projective model structures on categories of diagrams in a model category are introduced. These allow one to choose only a subset of the entries when defining weak equivalences, or to…
General relativity does not allow one to specify the topology of space, leaving the possibility that space is multi-- rather than simply--connected. We review the main mathematical properties of multi--connected spaces, and the different…
In this paper, I will discuss the geometrical structures of multipartite quantum systems based on complex projective schemes. In particular, I will explicitly construct multi-qubit states in terms of these schemes and also discuss…
Framed combinatorial topology is a novel theory describing combinatorial phenomena arising at the intersection of stratified topology, singularity theory, and higher algebra. The theory synthesizes elements of classical combinatorial…
Inspired by the realignment or computable cross norm criterion, we present a new result about the characterization of quantum entanglement. Precisely, an interesting class of inequalities satisfied by all separable states of a bipartite…
We define a computational type theory combining the contentful equality structure of cartesian cubical type theory with internal parametricity primitives. The combined theory supports both univalence and its relational equivalent, which we…
We introduce and study the notion of plurisubharmonic functions in calibrated geometry. These functions generalize the classical plurisubharmonic functions from complex geometry and enjoy their important properties. Moreover, they exist in…
A projective rectangle is like a projective plane that has different lengths in two directions. We develop the basic theory of projective rectangles including incidence properties, projective subplanes, configuration counts, a partial…
A theory of graded manifolds can be viewed as a generalization of differential geometry of smooth manifolds. It allows one to work with functions which locally depend not only on ordinary real variables, but also on $\mathbb{Z}$-graded…
We exhibit a computational type theory which combines the higher-dimensional structure of cartesian cubical type theory with the internal parametricity primitives of parametric type theory, drawing out the similarities and distinctions…
We present a generalization of multiview varieties as closures of images obtained by projecting subspaces of a given dimension onto several views, from the photographic and geometric points of view. Motivated by applications in Computer…
Several notions of multiplicativity are introduced for forms of degree $d\geq 3$ over a field of characteristic 0 or greater than d. Examples of multiplicative and strongly multiplicative forms of higher degree are given. Conditions…
In this article we survey recent results on rigid dualizing complexes over commutative algebras. We begin by recalling what are dualizing complexes. Next we define rigid complexes, and explain their functorial properties. Due to the…
The notions of $k$-separability and $k$-producibility are useful and expressive tools for the characterization of entanglement in multipartite quantum systems, when a more detailed analysis would be infeasible or simply needless. In this…
Certain many-particle Hardy inequalities are derived in a simple and systematic way using the so-called ground state representation for the Laplacian on a subdomain of $\mathbb{R}^n$. This includes geometric extensions of the standard Hardy…