Related papers: Jacobian of meromorphic curves
We interpret a formula for meromorphic functions on foliations by Riemann surfaces as an analogue to the product formula of valuations in algebraic number theory.
We discuss the integrability of Jacobi manifolds by contact groupoids, and then look at what the Jacobi point of view brings new into Poisson geometry. In particular, using contact groupoids, we prove a Kostant-type theorem on the…
In this paper, we give a universal family of curves of genus 2 whose jacobians have $\sqrt2$ multiplication fixed by the Rosati involution, and several results based on it, including isogenies between jacobians of curves, and jacobians of…
The aim of this paper is to develop a Hamilton--Jacobi theory for contact Hamiltonian systems. We find several forms for a suitable Hamilton-Jacobi equation accordingly to the Hamiltonian and the evolution vector fields for a given…
In a recent paper a class of infinite Jacobi matrices with discrete character of spectra has been introduced. With each Jacobi matrix from this class an analytic function is associated, called the characteristic function, whose zero set…
We construct relatively bounded toroidal and toric models of relatively bounded fibrations over curves.
We discuss the structure of the endomorphism algebras of the jacobians of superelliptic curves y^q=f(x) where q is a prime power and f(x) is an irreducible cubic or quartic polynomial over the field of rational functions k(t) in…
Let $C:f=0$ be a reduced curve in the complex projective plane. The minimal degree $mdr(f)$ of a Jacobian syzygy for $f$, which is the same as the minimal degree of a derivation killing $f$, is an important invariant of the curve $C$, for…
In this notes we study complex projective plane curves whose graded module of Jacobian syzygies is generated by its minimal degree component. Examples of such curves include the smooth curves as well as the maximal Tjurina curves. However,…
Let $\mathcal{C}$ be a smooth, projective, genus $g\geq 2$ curve, defined over $\mathbb{C}$. Then $\mathcal{C}$ has \emph{many automorphisms} if its corresponding moduli point $p \in \mathcal{M}_g$ has a neighborhood $U$ in the complex…
A set of multi-homogeneous equations for the Jacobian of a genus two curve is given. The approach used is to write down affine equations for the Jacobian minus various tranlations of the Theta-divisor by [2]-division points, and then to…
We use a combinatorial result relating the discriminant of the cycle pairing on a weighted finite graph to the eigenvalues of its Laplacian to deduce a formula for the orders of component groups of Jacobians of modular curves arising from…
Let $m\geq3$ be an integer. We show that every torsor of the Jacobian of the universal family of degree-$m$ Fermat curve is necessarily a connected component of the Picard scheme. We show that the Jacobian of the generic degree-$m$ Fermat…
This work studies the Jacobians of certain singular transformations and the corresponding measures which support the jacobian computations.
Originally, an abelian function field is the field of meromorphic functions on the Jacobi variety J(X) of a compact Riemann surface X. It is generated by the fundamental abelian functions belonging to the meromorphic function field on X. We…
We prove that in most cases relevant to cryptography, the Frobenius endomorphism on the Jacobian of a genus two curve is represented by a diagonal matrix with respect to an appropriate basis of the subgroup of l-torsion points. From this…
Let $f(x)$ be a degree $(2g+1)$ monic polynomial with coefficients in an algebraically closed field $K$ with $char(K)\ne 2$ and without repeated roots. Let $\mathfrak{R}\subset K$ be the $(2g+1)$-element set of roots of $f(x)$. Let…
In this present paper, we study the splitting of nodal plane curves with respect to contact conics. We define the notion of splitting type of such curves and show that it can be used as an invariant to distinguish the embedded topology of…
The connection between Jacobi fields and odular structures of affine manifold is established. It is shown that the Jacobi fields generate the natural geoodular structure of affinely connected manifolds.
We study the intersection cohomology of the theta divisors on Jacobians of nonhyperelliptic curves.