Related papers: An Extended Abel-Jacobi Map

We suggest an approach for description of integrable cases of the Abel equations. It is based on increasing of the order of equations up to the second one and using equivalence transformations for the corresponding second-order ordinary…

Let $C$ be a nonsingular complex projective curve, and $\mathcal{L}$ e a line bundle of degree 1 on $C$. Let $\mathcal{M}_{\alpha} := \mathcal{M}(r,\mathcal{L},\alpha)$ denote the moduli space of $S$-equivalence classes of Parabolic stable…

We present new properties of generalized core-EP inverse in a Banach *-algebra. We characterize this new generalized inverse by using involved annihilators. The generalized core-EP inverse for products is obtained. The core-EP orders for…

Algorithmic methods for the explicit inversion of the indefinite double covering maps are proposed. These are based on either the Givens decomposition or the polar decomposition of the given matrix in the proper, indefinite orthogonal group…

We prove that a polynomial map is invertible if and only if some associated differential ring homomorphism is bijective. To this end, we use a theorem of Crespo and Hajto linking the invertibility of polynomial maps with Picard-Vessiot…

The Abel-Jacobi map of the family of elliptic quintics lying on a general cubic threefold is studied. It is proved that it factors through a moduli component of stable rank 2 vector bundles on the cubic threefold with Chern numbers c_1=0,…

Let $X$ be a compact Riemann surface of genus $g$. Jacobi's inversion theorem states that the Abel-Jacobi map $\varphi : X^{(g)} \longrightarrow J(X)$ is surjective, where $X^{(g)}$ is the symmetric product of $X$ of degree $g$ and $J(X)$…

Convergence problems in coupled-cluster iterations are discussed, and a new iteration scheme is proposed. Whereas the Jacobi method inverts only the diagonal part of the large matrix of equation coefficients, we invert a matrix which also…

An important invariant of a polynomial $f$ is its Jacobian algebra defined by its partial derivatives. Let $f$ be invariant with respect to the action of a finite group of diagonal symmetries $G$. We axiomatically define an orbifold…

Let $X$ be a compact connected Riemann surface of genus at least two. The Abel-Jacobi map $\varphi: {\rm Sym}^d(X) \rightarrow {\rm Pic}^d(X)$ is an embedding if $d$ is less than the gonality of $X$. We investigate the curvature of the…

The Jacobian conjecture over a field of characteristic zero is considered directly in view of the nonlinear partial differential equations it is associated with. Exploring the integrals of such partial differential equations, this work…

We define certain extensions of Jacobi groups of $A_n$, prove an analogue of Chevalley Theorem for their invariants, and construct a Dubrovin Frobenius structure on it orbit space.

In this paper, we consider boundary extensions of two classes of mappings between metric measure spaces. These two mapping classes extend in particular the well-studied geometric mappings such as quasiregular mappings with integrable…

The multi-indexed Jacobi polynomials are the main part of the eigenfunctions of exactly solvable quantum mechanical systems obtained by certain deformations of the P\"oschl-Teller potential (Odake-Sasaki). By fine-tuning the parameter(s) of…

Linear differential equations with polynomial coefficients over a field $K$ of positive characteristic $p$ with local exponents in the prime field have a basis of solutions in the differential extension $\mathcal{R}_p=K(z_1, z_2,…

In this paper we use the orbital normal form of the nondegenerate Hopf-zero singularity to obtain necessary conditions for the existence of first integrals for such singularity. Also, we analyze the relation between the existence of first…

We consider a periodic Jacobi operator $H$ with finitely supported perturbations on ${\Bbb Z}.$ We solve the inverse resonance problem: we prove that the mapping from finitely supported perturbations to the scattering data: the inverse of…

Using an approach to the Jacobian Conjecture by L.M. Dru\.zkowski and K. Rusek 12], G. Gorni and G. Zampieri [19], and A.V. Yagzhev[27], we describe a correspondence between finite dimensional symmetric algebras and homogeneous tuples of…

The formula of expanding the Abel variety theta function restricted to Abel subvariety into theta functions of this subvariety is obtained. With the help of this formula the solution of differential equations with Jacobi theta functions,…

In this paper we introduce the generalized inverse of complex square matrix with respect to other matrix having same size. Some of its representations, properties and characterizations are obtained. Also some new representation matrices of…