In earlier papers [Wilson 04, Totaro 04], the S-invariant of a ternary cubic f was interpreted in terms of the curvature of related Riemannian and pseudo-Riemannian metrics — this is clarified further in Section 1. In the case when f arises from the cubic form on the second cohomology of a smooth projective threefold with second Betti number three, the value of the S-invariant is closely linked...

We prove that if [Formula: see text] is a reduced curve germ on rational surface singularity then its delta invariant can be recovered by concrete expression associated with the embedded topological type of pair text]. Furthermore, we also identify it another (a priori) analytic invariant, which motivated theory adjoint ideals. Finally, connect our formulae local correction term at singular poi...

Identifying PSL(2,C) as a projective group for patterns in the conformal camera model, the projective harmonic analysis on its double covering group SL(2,C) is presented in the noncompact and compact pictures–the pictures used to study different aspects of irreducible unitary representations of semisimple Lie groups. Bypassing technicalities of representation theory, but stressing the motivatio...

In this paper, we associate an invariant αx(L) to an algebraic point x on an algebraic variety X with an ample line bundle L. The invariant α measures how well x can be approximated by rational points on X , with respect to the height function associated to L. We show that this invariant is closely related to the Seshadri constant ǫx(L) measuring local positivity of L at x, and in particular th...

A contact path geometry is a family of paths in a contact manifold each of which is everywhere tangent to the contact distribution and such that given a point and a one-dimensional subspace of the contact distribution at that point there is a unique path of the family passing through the given point and tangent to the given subspace. A contact projective structure is a contact path geometry the...

A contact path geometry is a family of paths in a contact manifold each of which is everywhere tangent to the contact distribution and such that given a point and a one-dimensional subspace of the contact distribution at that point there is a unique path of the family passing through the given point and tangent to the given subspace. A contact projective structure is a contact path geometry the...

Purpose – In the literature, there is a lack of tools able to catch the symbolic dimension of the brand image, which go beyond rational and emotional dimensions. This paper aims to find and test a new instrument, named “Multi-Sensory Sort” (MuSeS). Design/methodology/approach – MuSeS, a direct methodology of exploring the consumer’s symbolic universe and the unconscious expectations, is compose...

The determination of invariant characteristics is an important problem in pattern recognition. Many invariants are known: Hu's moment invariants are invariant to shifts, to changes of scale, and to rotations [Hu62]; Burkhardt's Fourier descriptors to shifts, to changes of scale and to rotations [Bu79]; Arbter's Fourier descriptors to a ne transformations [Ar90]; Wang's invariant moments to a ne...

We are interested in the applications of invariant theory to computer vision problems. A survey and clariication of the diierent invariant calculation methods are detailed in our extented technical report 1]. In this paper, we concentrate on 3D invariants from pairs of images instead of invariants related to the planar projective transformations from monocular image, that have been already larg...

The Nagano-Yagi-Goldmann theorem states that on the torus T, every affine (or projective) structure is invariant or is constructed on the basis of some Goldmann rings [N-Y]. It shows the interest to study the invariant affine structure on the torus T or on abelian Lie groups. Recently, the works of Kim [K] and Dekempe-Ongenae [D-O] precise the number of non equivalent invariant affine structure...