相关论文: Essential coordinate components of characteristic …
This note aims at obtaining a variational characterization of complex structures by means of a calculus of variations for real vector bundle valued differential forms, and outlines a perspective to study existence questions via functionals…
We describe a family of hyperbolic knots whose character variety contain exactly two distinct components of characters of irreducible representations. The intersection points between the components carry rich topological information. In…
This paper presents the first approach to visualize the importance of topological features that define classes of data. Topological features, with their ability to abstract the fundamental structure of complex data, are an integral…
Normally we judge Topological shapes analytically but they hide significant amount of data in them about coordinate planes and ordered & unordered paris. In this article we will build our intuition and find those datas.
This paper announces results on the behavior of some important algebraic and topological invariants --- Euler characteristic, arithmetic genus, and their intersection homology analogues; the signature, etc. --- and their associated…
We prove that the irreducible components of the characteristic varieties of quasi-projective manifolds are either pull-backs of such components for orbifolds, or torsion points. This gives an interpretation for the so-called…
We define the characteristic numbers of a holomorphic k-distribution of any dimension on $mathbb P^n$ and obtain relations between these numbers and the characteristic numbers of an invariant subvariety. As an application we bound the…
The main purpose of this paper is to give a topological and symplectic classification of completely integrable Hamiltonian systems in terms of characteristic classes and other local and global invariants.
We give a geometric approach to the relation between the irreducible components of the characteristic varieties of local systems on a plane curve arrangement complement and the associated pencils of plane curves discovered recently by M.…
The spatial character of territorial systems plays a crucial role in the emergence of their complexities. This contribution aims at illustrating to what extent different types of complexities can be exhibited in models of such systems. We…
Each complex network (or class of networks) presents specific topological features which characterize its connectivity and highly influence the dynamics of processes executed on the network. The analysis, discrimination, and synthesis of…
These are notes from a basic course in Several Complex Variables
In this paper we determine topologically the canonical component of the $SL_2(\mathbb{C})$ character variety of the Whitehead link complement.
A survey of properties of a sequence of coefficients appearing in the evaluation of a quartic definite integral is presented. These properties are of analytical, combinatorial and number-theoretical nature.
Characteristic elements of the Tits algebra of a real hyperplane arrangement carry information about the characteristic polynomial. We present this notion and its basic properties, and apply it to derive various results about the…
We study the cone of effective divisors and the total coordinate ring of wonderful varieties, with applications to their automorphism group. We show that the total coordinate ring of any spherical variety is obtained from that of the…
A new look on the principal component analysis has been presented. Firstly, a geometric interpretation of determination coefficient was shown. In turn, the ability to represent the analyzed data and their interdependencies in the form of…
In this paper we present two intrinsic algebraic definitions of tropical variety motivated by the classical Zariski correspondence, one utilizing the algebraic structure of the coordinate semiring of an affine supertropical algebraic set,…
We introduce in this paper a hypercohomology version of the resonance varieties and obtain some relations to the characteristic varieties of rank one local systems on a smooth quasi-projective complex variety $M$, see Theorem (3.1) and…
The (homogeneous) Essentially Isolated Determinantal Variety is the natural generalization of generic determinantal variety, and is fundamental example to study non-isolated singularities. In this paper we study the characteristic classes…