Related papers: Characteristic Numbers and invariant subvarieties …

By discussing the Cauchy problem, we determine the covariant equation of the characteristic hypersurfaces in a relativistic superfluid theory.

Statistical models for genetic linkage analysis of k-locus diseases are k-dimensional subvarieties of a (3^k-1)-dimensional probability simplex. We determine the algebraic invariants of these models with general characteristics for k=1, in…

We define a special type of hypersurface varieties inside $\mathbb{P}_k^{n-1}$ arising from connected planar graphs and then find their equivalence classes inside the Gr\"othendieck ring of projective varieties. Then we find a…

We give a simple analytic criterion which characterizes linearizable 1-codimensional webs. Then we give an invariant geometrical interpretation of it, in term of projective connection. We explain then how our approach allows to study…

We investigate the common underlying discrete structures for various smooth and discrete nets. The main idea is to impose the characteristic properties of the nets not only on elementary quadrilaterals but also on larger parameter…

In this paper, we compute the Tian-Zhu invariant on hypersurfaces of complex projective spaces.

The present work is concerned with characterizing some algebraic invariants of edge ideals of hypergraphs. To this aim, firstly, we introduce some kinds of combinatorial invariants similar to matching numbers for hypergraphs. Then we…

Phylogenetic invariants are certain polynomials in the joint probability distribution of a Markov model on a phylogenetic tree. Such polynomials are of theoretical interest in the field of algebraic statistics and they are also of practical…

An invariant characterization of the rotationally symmetric R-separable webs for the Laplace equation in Euclidean space is given in terms of invariants and covariants of a real binary quartic canonically associated to the characteristic…

In this note we give an algebraic and topological interpretation of essential coordinate components of characteristic varieties and illustrate their importance with an example.

For a projective variety X defined over a field K, there is a special class of self-morphisms of X called algebraic dynamical systems. In this paper we take K to be the function field of a smooth curve and prove that at each place of K,…

We develop the theory of probabilistic variants of the one-category and diagonal topological complexity, which bound the classical LS-category and topological complexity from below. Unlike any other classical or probabilistic invariants,…

A class of cubic networks composed of a regular one-dimensional lattice and a set of long-range links is introduced. Networks parametrized by a positive integer k are constructed by starting from a one-dimensional lattice and iteratively…

Statistical Topology emerged since topological aspects continue to gain importance in many areas of physics. It is most desirable to study topological invariants and their statistics in schematic models that facilitate the identification of…

We show that Horrock's criterion for the splitting of vector bundles on $\PP^n$ can be extended to vector bundles on multiprojective spaces and to smooth projective varieties with the weak CM property (see Definition 3.11). As a main tool…

Invariants for Riemann surfaces covered by the disc and for hyperbolic manifolds in general involving minimizing the measure of the image over the homotopy and homology classes of closed curves and maps of the $k$-sphere into the manifold…

Let G/H be a semisimple symmetric space. The main tool to embed a principal series representation of G into L^2(G/H) are the H-invariant distribution vectors. If G/H is a non-compactly causal symmetric space, then G/H can be realized as a…

The characteristic numbers of smooth plane quartics are computed using intersection theory on a component of the moduli space of stable maps. This completes the verification of Zeuthen's prediction of characteristic numbers of smooth plane…

Let f be a non-invertible holomorphic endomorphism of the complex projective space P^k and f^n its iterate of order n. Let V be an algebraic subvariety of P^k which is generic in the Zariski sense. We give here a survey on the asymptotic…

Characteristic scale is a notion that pervades the geophysical sciences, but it has no widely accepted precise definition. The wavelet transform decomposes a time series into coefficients that are associated with different scales. The…