To a symmetric, relatively ample line bundle on an abelian scheme one can associate a linear combination of the determinant bundle and the relative canonical bundle, which is a torsion element in the Picard group of the base. We improve the bound on the order of this element found by Faltings and Chai. In particular, we obtain an optimal bound when the degree of the line bundle d is odd and the...

Universidad Autónoma de Zacatecas 13.1 Equivalent Circuit ........................................................... 13-1 13.2 Resistance ......................................................................... 13-2 Frequency Effect . Temperature Effect . Spiraling and Bundle Conductor Effect 13.3 Current-Carrying Capacity (Ampacity) ........................ 13-5 13.4 Inductance and Inductive...

Let K denote a closed odd-dimensional smooth manifold and let E be a flat vector bundle over K. In this situation the construction of Ray and Singer [RS] gives a metric on the determinant line of the cohomology detH(M ;E) which is a smooth invariant of the manifold M and the flat bundle E. (Note that if the dimension of K is even then the Ray-Singer metric depends on the choice of a Riemannian ...

It is shown how the coherent states permit to find different geometrical objects as the geodesics, the conjugate locus, the cut locus, the Calabi’s diastasis and its domain of definition, the Euler-Poincaré characteristic, the number of Borel-Morse cells, the Kodaira embedding theorem. 1 Coherent state manifold and coherent vector manifold In this talk the coherent states [] are presented as a ...

In this paper, we study the equations of projectively embedded abelian surfaces with a polarization of type (1; d). Classical results say that given an ample line bundle L on an abelian surface A, the line bundle L n is very ample for n 3, and furthermore, in case n is even and n 4, the generators of the homogeneous ideal I A of the embedding of A via L n are all quadratic; a possible choice fo...

Based on the transmission line model (TLM), we present an exact and general transfer function formula, useful for both single multiwall carbon nanotube (MWCNT) and MWCNT bundle interconnects. Using the standard parameters for 22-nm technology node we perform the Nyquist stability analysis, to investigate the dependence of the degree of relative stability for both single and bundle interconnects...

From many earlier works on the classification theory of compact complex manifolds and their intrinsic geometric structures, it has been clear that “positivity” or “nonpositivity” properties of subsheaves of exterior powers of the tangent or cotangent bundle provide some of the most important global information concerning the manifold in question. The programs of Iitaka and Mori on a general cla...

As the loop space of a Riemannian manifold is infinite-dimensional, it non-trivial problem to make sense “top degree component” differential form on it. In this paper, we show that formula from finite dimensions generalizes assign sensible certain composite forms, obtained by wedging with exponential (in exterior algebra) canonical presymplectic 2-form space. This construction crucial ingredien...

From many earlier works on the classification theory of compact complex manifolds and their intrinsic geometric structures, it has been clear that “positivity” or “nonpositivity” properties of subsheaves of exterior powers of the tangent or cotangent bundle provide some of the most important global information concerning the manifold in question. The programs of Iitaka and Mori on a general cla...