Related papers: The Jacobian of a nonorientable Klein surface, II
In the previous article, we showed the Rasmussen-Tamagawa conjecture for QM-abelian surfaces over imaginary quadratic fields. In this article, we generalize the previous work to QM-abelian surfaces over number fields of higher degree. We…
We study finite dimensional semisimple Hopf algebra actions on noetherian connected graded Artin-Schelter regular algebras, and introduce definitions of the Jacobian, the reflection arrangement and the discriminant in a noncommutative…
In this paper we define a Grassmann odd analogue of Jacobi structure on a supermanifold. The basic properties are explored. The construction of odd Jacobi manifolds is then used to reexamine the notion of a Jacobi algebroid. It is shown…
We examine \'etale covers of genus two curves that occur in the linear system of a polarizing line bundle of type $(1,d)$ on a complex abelian surface. We give results counting fixed points of involutions on such curves as well as…
Let $X$ be a proper, smooth, and geometrically connected curve over a non-archimedean local field $K$. In this paper, we relate the component group of the N\'eron model of the Jacobian of $X$ to the Brauer group of $X$.
Recent developments of affine algebraic geometry, especially the theory of open algebraic surfaces, provide means to systematically explore geometric and topological properties of polynomials in two variables. Nevertheless, there is one…
Some general problems of Jacobian computations in non-full rank matrices are discussed in this work. In particular, the Jacobian of the Moore-Penrose inverse derived via matrix differential calculus is revisited. Then the Jacobian in the…
We study Nurikabe puzzles on non-orientable surfaces. Specifically, we propose two versions of non-orientable Nurikabe and investigate their combinatorics on M\"obius strips, Klein bottles, and projective planes of size $1\times n$. Our…
This paper has been withdrawn by the author due to an erro thereon line -2 of page 4.
The aim of this paper is to extend our old results about Galois action on the torsion points of abelian varieties to the case of (finitely generated) fields of characteristic 2.
We state two recent results concerning the linearization of integrable systems on generalised Jacobians. Then we apply this to the (complexified) spherical pendulum.
We give two characterizations of Jacobians of curves with involution having fixed points in the framework of two particular cases of Welter's trisecant conjecture. The geometric form of each of these characterizations is the statement that…
Let $S$ be a compact Riemann surface and let $H$ be a finite group. It is known that if $H$ acts on $S$ then there is a $H$-equivariant isogeny decomposition of the Jacobian variety $JS$ of $S,$ called the group algebra decomposition of…
The main purpose of this paper is to give an overview over the theory of abelian varieties, with main focus on Jacobian varieties of curves reaching from well-known results till to latest developments and their usage in cryptography. In the…
This is a short addendum to a note of Beauville on the subject of the title. We prove an inequality that takes into account the constant part of the Jacobian.
A definition of non-abelian genus zero open Wilson surfaces is proposed. The ambiguity in surface-ordering is compensated by the gauge transformations.
Using a new type of Jacobi field estimate we will prove a duality theorem for singular Riemannian foliations in complete manifolds of nonnegative sectional curvature.
Given a Klein surface Y, there is a unique symmetric Riemann surface X being the complex double of Y. In this paper we shall show that the situation is not the same when we work in the category of surfaces with nodes.
The starting point of this note is our recent paper with Laza and Sacc\`a on the construction of deformations of O'Grady's $10$-dimensional manifolds as compactifications of intermediate Jacobian fibrations associated to cubic fourfolds.…
The aim of the present paper is the study of real hypersurfaces equipped with the condition $\phi l = l \phi$, $l = R(., \xi, \xi)$.