相关论文: Geometry of superficial elements
We review aspects of an important paper by Robert Strichartz concerning reverse iterated function systems (i.f.s.) and fractal blowups. We compare the invariant sets of reverse i.f.s. with those of more standard i.f.s. and with those of…
To, say, a proper algebraic or holomorphic space $X/S$, and a coherent sheaf ${\mathcal F}$ on $X$ we identify a functorial ideal, the fitted flatifier, blowing up sequentially in which leads to a flattening of the proper transform of…
This book is an introduction to the nascent field of Fourier analysis on polytopes, and cones. There is a rapidly growing number of applications of these methods, so it is appropriate to invite students, as well as professionals, to the…
In this letter, we report on an analytical technique for optical investigations of semitransparent samples. By Fourier transforming optical spectra with Fabry-Perot resonances we extract information about sample thickness and its discrete…
We introduce the concept of effective geometry by studying several systems in which it arises naturally. As an example of the power and conciseness of the method, it is shown that a flowing dielectric medium with a linear response to an…
We prove the algebraic version of a conjecture of C. Sabbah on the existence of the good formal structure for meromorphic flat connections on surfaces after some blow up.
Consider a complex projective space with its Fubini-Study metric. We study certain one parameter deformations of this metric on the complement of an arrangement (=a finite union of hyperplanes) whose Levi-Civita connection is of Dunkl…
This is the second paper in a series of papers aimed at providing a geometric construction of modular functors and topological quantum field theories from conformal field theory building on the constructions in [TUY] and [KNTY]. We give a…
The problem of evaluating potential integrals on planar triangular elements has been addressed using a polar coordinate decomposition. The resulting formulae are general, exact, easily implemented, and have only one special case, that of a…
Let $X$ be a fixed projective scheme which is flat over a base scheme $S$. The association taking a quasi-projective $S$-scheme $Y$ to the scheme parametrizing $S$-morphisms from $X$ to $Y$ is functorial. We prove that this functor…
We develop some basic facts on deformations of exterior differential ideals on a smooth complex algebraic variety. With these tools we study deformations of several types of differential ideals, leading to several irreducible components of…
Fixed a point O on a non-singular surface S and a complete mO-primary ideal I in its local ring, the curves on the surface X obtained by blowing-up I are studied in terms of the base points of I. Criteria for the principality of these…
A central problem of geometry is the tiling of space with simple structures. The classical solutions, such as triangles, squares, and hexagons in the plane and cubes and other polyhedra in three-dimensional space are built with sharp…
For a locally compact abelian group $G$, J. L. Taylor (1971) gave a complete characterization of invertible elements in the measure algebra $M(G)$. Using the Fourier-Stieltjes transform, this characterization can be carried out in the…
We study the dependence of geometric invariant theory quotients on the choice of a linearization. We show that, in good cases, two such quotients are related by a flip in the sense of Mori, and explain the relationship with the minimal…
In contrast to that a weak value of an observable is usually divided into real and imaginary parts, here we show that separation into modulus and argument is important for modular values. We first show that modular values are expressed by…
Evaluation of the angular distribution function of particles scattered in an amorphous medium is improved by deforming the integration path in the Fourier integral representation into the complex plane. That allows us to present the…
We consider deformations of bounded complexes of modules for a profinite group G over a field of positive characteristic. We prove a finiteness theorem which provides some sufficient conditions for the versal deformation of such a complex…
In this expositional paper, we discuss commutative algebra -- a study inspired by the properties of integers, rational numbers, and real numbers. In particular, we investigate rings and ideals, and their various properties. After, we…
A module $M$ over the tropical semifield $T$ is analogous to a module over a field. We assume that $M$ is straight reflexive, and define the dimension of $M$ to the number of elements of a basis. We study the dimension of a straight…