Related papers: On Clifford dimension for singular curves
Clifford indices for semistable vector bundles on a smooth projective curve of genus at least 4 were defined in previous papers of the authors. In the present paper, we establish lower bounds for the Clifford indices for rank 3 bundles. As…
We study concepts of stabilities associated to a smooth complex curve together with a linear series on it. In particular we investigate the relation between stability of the associated Dual Span Bundle and linear stability. Our result…
We study torsion free sheaves on integral projective curves with at most ordinary cusps as singularities. Adjusting Seshadri's structure from the nodal case to this one, we describe these sheaves by means of a triple defined in the…
It has been a long-standing problem to find an adequate definition of a Clifford index for higher rank vector bundles on curves, which should capture the complexity of the curve in its moduli space. An interesting proposal in rank 2 has…
I apply the algebraic framework developed in [1] to study geometry of hyperbolic spaces in 1, 2, and 3 dimensions. The background material on projectivised Clifford algebras and their application to Cayley-Klein geometries is described in…
We study the algebra of complex polynomials which remain invariant under the action of the local Clifford group under conjugation. Within this algebra, we consider the linear spaces of homogeneous polynomials degree by degree and construct…
We give a Clifford correspondence for an algebra A over an algebraically closed field, that is an algorithm for constructing some finite-dimensional simple A-modules from simple modules for a subalgebra and endomorphism algebras. This…
We consider the extension of the Jackson calculus into higher dimensions and specifically into Clifford analysis.
These are lecture notes for a course on the theory of Clifford algebras, with special emphasis on their wide range of applications in mathematics and physics. Clifford algebra is introduced both through a conventional tensor algebra…
The Sylvester equation and its particular case, the Lyapunov equation, are widely used in image processing, control theory, stability analysis, signal processing, model reduction, and many more. We present basis-free solution to the…
We functorially identify similarity classes of line-bundle-valued quadratic forms on rank two vector bundles with isomorphism classes of pairs consisting of the degree zero and the degree one parts of the associated generalized Clifford…
We consider singularities of frontal surfaces of corank one and finite frontal codimension. We look at the classification under left-right-equivalence and introduce the notion of frontalisation for singularities of fold type. We define the…
The Clifford spectrum is a form of joint spectrum for noncommuting matrices. This theory has been applied in photonics, condensed matter and string theory. In applications, the Clifford spectrum can be efficiently approximated using…
Let $(X,H)$ be a polarized K3 surface with $\mathrm{Pic}(X) = \mathbb Z H$, and let $C\in |H|$ be a smooth curve of genus $g$. We give an upper bound on the dimension of global sections of a semistable vector bundle on $C$. This allows us…
We give an inductive construction for irreducible Clifford systems on Euclidean vector spaces. We then discuss how this notion can be adapted to Riemannian manifolds, and outline some developments in octonionic geometry.
We give examples of curves of arbitrarily high Clifford index such that the Prym map is not injective at any of their \'etale double covers.
We prove that the Clifford spectrum associated to three 2 by 2 matrices is nonempty. The structure of Clifford is described in terms "moving" level curves. We discuss some implication of a conjecture formulated for arbitrary size n by n of…
The Clifford algebra of a n-dimensional Euclidean vector space provides a general language comprising vectors, complex numbers, quaternions, Grassman algebra, Pauli and Dirac matrices. In this work, we present an introduction to the main…
We study briefly some properties of real Clifford algebras and identify them as matrix algebras. We then show that the representation space on which Clifford algebras act are spinors and we study in details matrix representations. The…
We show, among other things, that in most cases the gonality of a subcanonical curve in projective-three space is computable by multisecants.