Related papers: Calculations with Characteristic Cycles
We give a formula for computing the characteristic polynomial for certain hyperplane arrangements in terms of the number of bipartite graphs of given rank and cardinality.
We obtain sharp bounds for the number of n--cycles in a finite graph as a function of the number of edges, and prove that the complete graph is optimal in more ways than could be imagined. We prove sharp estimates on both the sum of k-th…
By discussing the Cauchy problem, we determine the covariant equation of the characteristic hypersurfaces in a relativistic superfluid theory.
We study a class of holomorphic matrix models. The integrals are taken over middle dimensional cycles in the space of complex square matrices. As the size of the matrices tends to infinity, the distribution of eigenvalues is given by a…
In the first part of this article, we consider ruled surfaces defined over a finite field; we introduce invariants for them, and describe some explicit contructions that illustrate possible behaviour of these invariants. In the second part,…
In this paper, we find a full description of concircular hypersurfaces in space forms as a special family of ruled hypersurfaces. We also characterize concircular helices in 3-dimensional space forms by means of a differential equation…
In this paper we give a characterization of the height of K3 surfaces in positive characteristic. This enables us to calculate the cycle classes of the loci in families of K3 surfaces where the height is at least h. The formulas for such…
We derive various interesting properties of complex equiangular cyclic frames for many pairs (n, k) using Gauss sums and number theory. We further use these results to study the random and burst errors of some special cases of complex…
Formulas to calculate multivector exponentials in a base-free representation and in a orthonormal basis are presented for an arbitrary Clifford geometric algebra Cl(p,q). The formulas are based on the analysis of roots of characteristic…
We present some results on character degree sums in connection with certain characteristics of finite groups such as p-solvability, solvability, supersolvability, and nilpotency. Some of them strengthen known results in the literature.
With the help of hypergeometric functions over finite fields, we study some arithmetic properties of cyclotomic matrices involving characters and binary quadratic forms over finite fields. Also, we confirm some related conjectures posed by…
We study endomorphism rings of principally polarized abelian surfaces over finite fields from a computational viewpoint with a focus on exhaustiveness. In particular, we address the cases of non-ordinary and non-simple varieties. For each…
A study of triangulations of cycles in the Cayley diagrams of finitely generated groups leads to a new geometric characterization of hyperbolic groups.
A new family of maximal curves over a finite field is presented and some of their properties are investigated.
We define special cycles on arithmetic models of twisted Hilbert-Blumenthal surfaces at primes of good reduction. These are arithmetic versions of these cycles. In particular, we characterize the non-degenerate intersections and partially…
We construct highly singular projective curves and surfaces defined by invariants of primitive complex reflection groups.
We investigate the interplay between linear systems on curves and graphs in the context of specialization of divisors on an arithmetic surface. We also provide some applications of our results to graph theory, arithmetic geometry, and…
An abstract theory of ultradifferentiable sheafs is developed. Moreover, various applications to the theory of linear partial differential equations, differential geometry and, in particular, CR geometry are discussed.
We consider a model of random permutations of the sites of the cubic lattice. Permutations are weighted so that sites are preferably sent onto neighbors. We present numerical evidence for the occurrence of a transition to a phase with…
We prove two related concentration inequalities concerning the number of rational points of hyperelliptic curves over subsets of a finite field. In particular, we investigate the probability of a large discrepancy between the numbers of…