Some algebraic theorems on vector-valued forms and their geometric applications

Algebraic properties of some new vector-valued rational interpolants

In a recent paper of the author [A. Sidi,A new approach to vector-valued rational interpolation, J.Approx. Theory, 130 (2004) 177–187], three new interpolation procedures for vector-valued functions F(z), where F : C → CN , were proposed, and some of their properties were studied. In this work, after modifying their definition slightly, we continue the study of these interpolation procedures. W...

Some vector valued Siegel modular forms of genus 2

is a module over the ring of all modular forms with respect to the group Γ2[4, 8]. We are interested in its structure. By Igusa, the ring of modular forms is generated by the ten classical theta constants θ[m]. The module M contains a submodule N which is generated by 45 Cohen-Rankin brackets {θ[m], θ[n]}. We determine defining relations for this submodule and compute its Hilbert function (Theo...

Some vector valued Siegel modular forms of genus 3 Eberhard

Algebraic-geometric codes from vector bundles and their decoding

Algebraic-geometric codes can be constructed by evaluating a certain set of functions on a set of distinct rational points of an algebraic curve. The set of functions that are evaluated is the linear space of a given divisor or, equivalently, the set of section of a given line bundle. Using arbitrary rank vector bundles on algebraic curves, we propose a natural generalization of the above const...

Geometric Separator Theorems & Applications

| We nd a large number of \geometric separator theorems" such as: I: Given N disjoint iso-oriented squares in the plane, there exists a rectangle with 2N=3 squares inside, 2N=3 squares outside, and (4 + o(1)) p N partly in & out. II: There exists a rectangle that is crossed by the minimal spanning tree of N sites in the plane at (4 3 1=4 + o(1)) p N points, having 2N=3 sites inside and outside....