Related papers: Hesse Pencils and 3-Torsion Structures
Suppose X is a smooth projective 3-fold of general type and |mK_X| is composed of a pencil of surfaces with m>1. This pencil naturally induces a fibration f:X->C onto a smooth curve C after the Stein-factorization, which is the main objects…
We use slicing by nongeneric pencils of hypersurfaces and prove a new theorem of Lefschetz type for singular non compact spaces, at the homotopy level. As applications, we derive results on the topology of the fibres of polynomial functions…
We give a geometric approach to the relation between the irreducible components of the characteristic varieties of local systems on a plane curve arrangement complement and the associated pencils of plane curves discovered recently by M.…
We develop the necessary machinery in order to prove that hexagonal tilings are uniquely determined by their Tutte polynomial, showing as an example how to apply this technique to the toroidal hexagonal tiling.
We introduce a definition of strong hyperbolicity for second order partial differential equations using second order pencils. We show that this definition is equivalent to the standard one, derived by reducing the equations to first order…
The GKZ system for the Hesse pencil of elliptic curves has more solutions than the period integrals. In this work we give different realizations and interpretations of the extra solution, in terms of oscillating integral, Eichler integral,…
Hilbert schemes of suitable smooth, projective 3-fold scrolls over the Hirzebruch surface F_e, with e > 1, are studied. An irreducible component of the Hilbert scheme parametrizing such varieties is shown to be generically smooth of the…
We propose an effective geometrical approach to recover the normal form of a given Elasticity tensor, once we know its symmetry class. In other words, we produce a rotation which brings an Elasticity tensor onto its normal form, given its…
In analogy with the vector bundle theory we define universal and strongly universal Lefschetz fibrations over bounded surfaces. After giving a characterization of these fibrations we construct very special strongly universal Lefschetz…
The purpose of the present work is solving the characterization problem for one class of second order operator pencil with complex periodic coefficients, which consists of identification of necessary and sufficient conditions on the…
We give necessary and sufficient conditions on the curvature and the torsion of a regular curve of the space forms $\h^3$ and $\s^3$ to be contained in a totally umbilical surface. In case that the curve has constant torsion, we obtain the…
Pen pressure is an input channel typically available in tablet pen device. To date, little attention has been paid to the use of pressure in the domain of graphical interaction, its usage largely limited to drawing and painting program,…
We prove that every tetrahedron T has a simple, closed quasigeodesic that passes through three vertices of T. Equivalently, every T has a face whose "exterior angles" are at most pi.
The change of the Kronecker structure of a matrix pencil perturbed by another pencil of rank one has been characterized in terms of the homogeneous invariant factors and the chains of column and row minimal indices of the initial and the…
The aim of this article is to provide a complementary understanding to some results of the second author using the machinery of Koszul complexes, and to explain how this approach can provide a new description of projective derived…
We review the motivation and fundamental properties of the Hausdorff dimension of metric spaces and illustrate this with a number of examples, some of which are expected and well-known. We also give examples where the Hausdorff dimension…
We review the applications of twisted spectral triples to the Standard Model. The initial motivation was to generate a scalar field, required to stabilise the electroweak vacuum and fit the Higgs mass, while respecting the first-order…
We study problems associated with an operator pencil, i.e., a pair of operators on Banach spaces. Two natural problems to consider are linear constrained differential equations and the description of the generalized spectrum. The main tool…
This article studies germs of holomorphic vector fields at the origin of C3 that are tangent to holomorphic foliations of codimension one. Two situations are considered. First, we assume hypotheses on the reduction of singularities of the…
We have discovered that two significant quantities within hard particle systems: the probability of successfully inserting an additional particle at random and the scale distribution function, can be connected by a concise relation. We…