In this paper, we propose a new height function for a variety defined over a finitely generated field overQ. For this height function, we will prove Northcott’s theorem and Bogomolov’s conjecture, so that we can recover the original Raynaud’s theorem (Manin-Mumford’s conjecture). CONTENTS Introduction 1 1. Arakelov intersection theory 3 2. Arithmetically positive hermitian line bundles 6 3. Ari...

We investigate analytic properties of height zeta functions of toric bundles over flag varieties.

We propose a novel shape descriptor for matching and recognizing 2D object silhouettes. The contour of each object is represented by a fixed number of sample points. For each sample point, a height function is defined based on the distances of the other sample points to its tangent line. One compact and robust shape descriptor is obtained by smoothing the height functions. The proposed descript...