Related papers: The Jacobian of a nonorientable Klein surface, II
Using divisors, an analog of the Jacobian for a compact connected nonorientable Klein surface $Y$ is constructed. The Jacobian is identified with the dual of the space of all harmonic real one-forms on $Y$ quotiented by the torsion-free…
Let A be a principally polarized abelian threefold over a perfect field k, not isomorphic to a product over the algebraic closure of k. There exists a canonical extension k' of k, of degree 1 or 2, such that A becomes isomorphic to a…
In this paper we investigate a problem of approximation of continuous mappings by smooth mappings with nonnegative Jacobian.
We find explicit equations for two-coverings of Jacobians of genus two curves over an arbitrary ground field of characteristic different from two.
Based on the results people have obtained, we try to prove the Jacobian conjecture, but there is a gap in the proof.
We present some motivations and discuss various aspects of an approach to the Jacobian Conjecture in terms of irreducible elements and square-free elements.
A particular case of the Jacobian conjecture is considered and for small dimensional cases a computational approach is offered
This work studies the Jacobians of certain singular transformations and the corresponding measures which support the jacobian computations.
This paper is concerned with some Algebraic Geometry codes on Jacobians of genus 2 curves. We derive a lower bound for the minimum distance of these codes from an upper "Weil type" bound for the number of rational points on irreducible…
We prove surjectivity criteria for $p$-adic representations and we apply them to abelian varieties over number fields. In particular, we provide examples of Jacobians over $\dbQ$ of dimension $d\in\{1,2,3\}$ whose 2-adic representations…
Any counterexample to the two-dimensional Jacobian Conjecture gives a rational map from one projective plane to another. We use some ideas of the Minimal Model Program to study the combinatorial structure of a rational surface, that is…
We show that the Jacobian conjecture of the two dimensional case is true.
We introduce a new method in the attempt to prove the Jacobian conjecture. In the complex dimension 2 case, we apply this method to prove some new results related the Jacobian conjecture.
We study the structure of Jacobians of geometrically reduced curves over arbitrary (i. e., not necessarily perfect) fields. We show that, while such a group scheme cannot in general be decomposed into an affine and an Abelian part as over…
We investigate the 2-dimensional jacobian conjecture via Klein's program.
Generalizing a result for the binary lens, similar alternative expressions are also given for the Jacobian determinant for a gravitational lens consisting of an arbitrary number of discrete lensing centres, with arbitrary masses and…
This paper is the second in a series of two papers which study the phenomenon of tropical split Jacobians. The first paper is a contemplative study, embedded in the broader context of exploring connections between the category of tropical…
We define the Jacobian of a Riemann surface with analytically parametrized boundary components. These Jacobians belong to a moduli space of ``open abelian varieties'' which satisfies gluing axioms similar to those of Riemann surfaces, and…
An abelian surface A over a field K has potential quaternionic multiplication if the ring End_\bar K (A) of geometric endomorphisms of A is an order in an indefinite rational division quaternion algebra. In this brief note, we study the…
An important problem in computational arithmetic geometry is to find changes of coordinates to simplify a system of polynomial equations with rational coefficients. This is tackled by a combination of two techniques, called minimisation and…