Related papers: A note on Clifford parallelisms in characteristic …

The classical Clifford correspondence for normal subgroups is considered in the more general setting of semisimple Hopf algebras. We prove that this correspondence still holds if the extension determined by the normal Hopf subalgebra is…

Let $K$ be a local field with residue characteristic $p$ and let $L/K$ be a totally ramified extension of degree $p^k$. In this paper we show that if $L/K$ has only two distinct indices of inseparability then there exists a uniformizer…

There is a classical relationship in algebraic geometry between a hyperelliptic curve and an associated pencil of quadric hypersurfaces. We investigate symplectic aspects of this relationship, with a view to applications in low-dimensional…

Classification of quantum spinor fields according to quantum bilinear covariants is introduced in a context of quantum Clifford algebras on Minkowski spacetime. Once the bilinear covariants are expressed in terms of algebraic spinor fields,…

We study (4,4) supersymmetric field theories in two dimensions with a one dimensional Coulomb branch. These theories have applications in string theory. Our analysis explains the known relation between $A-D-E$ groups and modular invariants…

Geometry-based camera calibration using principal line is more precise and robust than calibration using optimization approaches; therefore, several researches try to re-derive the principal line from different views of 2D projective…

The main purpose in this paper is to study the gonality, the Clifford index and the Clifford dimension on linearly equivalent smooth curves on Enriques surfaces. The method is similar to techniques of M.Green $\&$ R.Lazarsfeld and…

We construct some infinite series of free and nearly free curves using pencils of conics with a base locus of cardinality at most two. These curves have an interesting topology, e.g. a high degree Alexander polynomial that can be explicitly…

The Clifford action on superspaces is analyzed with a view on generalized Dirac fields taking values in some Clifford supermodule. the stress is here on two principles: complexification and polarisation. For applications in field theory,…

This article presents the description of the internal spaces of fermion and boson fields in $d$-dimensional spaces, with the odd and even "basis vectors" which are the superposition of odd and even products of operators $\gamma^a$. While…

A plane curve on a the projective space over a field of characteristic zero is free if its associated sheaf T of tangent vector fields tangent is a free module. Relatively few free curves are known. Here we prove that a divisor consisting…

Based on a fact that complex Clifford algebras of even dimension are isomorphic to the matrix ones, we consider bundles in Clifford algebras whose structure group is a general linear group acting on a Clifford algebra by left…

A graph is apex if there is a vertex whose deletion makes the graph planar, and doublecross if it can be drawn in the plane with only two crossings, both incident with the infinite region in the natural sense. In 1966, Tutte conjectured…

We investigate connections between the geometry of linear subspaces and the convergence of the alternating projection method for linear projections. The aim of this article is twofold: in the first part, we show that even in Euclidean…

We provide a characterisation of differentially large fields in arbitrary characteristic and a single derivation in the spirit of Blum axioms for differentially closed fields. In the case of characteristic zero, we use these axioms to…

Let $d$ and $n$ be positive integers, and $E/F$ be a separable field extension of degree $m=\binom{n+d}{n}$. We show that if $|F| > 2$, then there exists a point $P\in \mathbb{P}^n(E)$ which does not lie on any degree $d$ hypersurface…

We consider several characterizations of $\mathbb R$-linear mappings. In particular, we give a characterization of linear mappings whose range is $\geq$ 2 dimensional, in terms of preservation of lines (and contraction of lines to a point)…

We prove in particular that the Lipschitz-free space over a finitely-dimensional normed space is complemented in its bidual. For Euclidean spaces the norm of the respective projection is $1$. As a tool to obtain the main result we establish…

Each vector space that is endowed with a quadratic form determines its Clifford algebra. This algebra, in turn, contains a distinguished group, known as the Lipschitz group. We show that only a quotient of this group remains meaningful in…

Given a real curve, we study special linear systems called "very special" for which the dimension does not satisfy a Clifford type inequality. We classify all these very special linear systems when the gonality of the curve is small.