On infinitesimal Strebel points

On the First Infinitesimal Neighborhood of a Linear Configuration of Points in P

We consider the following open questions. Fix a Hilbert function h, that occurs for a reduced zero-dimensional subscheme of P. Among all subschemes, X, with Hilbert function h, what are the possible Hilbert functions and graded Betti numbers for the first infinitesimal neighborhood, Z, of X (i.e. the double point scheme supported on X)? Is there a minimum (h) and maximum (h) such function? The ...

The Geometric Interpretation of Fröberg-iarrobino Conjectures on Infinitesimal Neighbourhoods of Points in Projective Space

The study of infinitesimal deformations of a variety embedded in projective space requires, at ground level, that of deformation of a collection of points, as specified by a zero-dimensional scheme. Further, basic problems in infinitesimal interpolation correspond directly to the analysis of such schemes. An optimal Hilbert function of a collection of infinitesimal neighbourhoods of points in p...

The Asymptotic Behavior of Jenkins-strebel Rays

In this paper, we consider the asymptotic behavior of two Teichmüller geodesic rays determined by Jenkins-Strebel differentials, and we obtain a generalization of a theorem by the author in On behavior of pairs of Teichmüller geodesic rays, 2014 . We also consider the infimum of the asymptotic distance up to choice of base points of the rays along the geodesics. We show that the infimum is repr...

Field Theory on Infinitesimal-Lattice Spaces

Equivalence in physics is discussed on the basis of experimental data accompanied by experimental errors. It is pointed out that the introduction of the equivalence being consistent with the mathematical definition is possible only in theories constructed on non-standard number spaces by taking the experimental errors as infinitesimal numbers. Following the idea for the equivalence, a new descr...

A Characterization of the Infinitesimal Conformal Transformations on Tangent Bundles