In this paper we discuss second-order properties of the Moreau-Yosida regularization F of a piecewise twice continuously differentiable convex function f . We introduce a new constraint qualification in order to prove that the gradient of F is piecewise continuously differentiable. In addition, we discuss conditions, depending on the Hessians of the pieces, that guarantee positive definiteness ...

Mumford defined a natural isomorphism between the intermediate jacobian of a conicbundle over P and the Prym variety of a naturally defined étale double cover of the discrminant curve of the conic-bundle. Clemens and Griffiths used this isomorphism to give a proof of the irrationality of a smooth cubic threefold and Beauville later generalized the isomorphism to intermediate jacobians of odd-di...

In the study of integrable systems of ODE’s arising from a Lax pair with a parameter, the constants of the motion occur as spectral curves. Many of these systems are algebraically completely integrable in that they linearize on the Jacobian of a spectral curve. In an earlier paper the authors gave a classification of the spectral curves in terms of the Weyl group and arranged the spectral curve...

M P = {A(x) ∈ M : det(A(x)− yIr) = P (x, y)}. The system (1) has an obvious symmetry group G = IPGLr(I C; J) which is the subgroup of the projective group IPGLr(I C) formed by matrices which commute with J . The group G acts on M by conjugation, the action is Poisson, and the reduced Hamiltonian system is completely integrable too. As the symmetry group G acts freely and properly on the general...

‎In a (t,n)-threshold secret sharing scheme‎, ‎a secret s is distributed among n participants such that any group of t or more participants can reconstruct the secret together‎, ‎but no group of fewer than t participants can do‎. In this paper, we propose a verifiable (t,n)-threshold multi-secret sharing scheme based on Shao and Cao‎, ‎and the intractability of the elliptic curve discrete logar...

We consider abelian varieties with a group of automorphisms isomorphic to generalized quaternion group. provide isogeny decompositions, compute dimensions the corresponding factors and give conditions under which this decomposition is nontrivial. then specialize our results Jacobians relate them so-called genus-zero actions on Riemann surfaces. A complete classification uniparametric families s...

We compute the subgroup of monodromy group a generalized Kummer variety associated to equivalences derived categories abelian surfaces. The result was previously announced in arXiv:1201.0031. Mongardi showed that constructed here is fact whole group. As an application we prove Hodge conjecture for generic fourfold Weil type with complex multiplication by arbitrary imaginary quadratic number fie...

We discuss approaches to computing in the Shafarevich-Tate group of Jacobians of higher genus curves, with an emphasis on the theory and practice of visualisation. Especially for hyperelliptic curves, this often enables the computation of ranks of Jacobians, even when the 2-Selmer bound does not bound the rank sharply. This was previously only possible for a few special cases. For curves of gen...

After discretization in time with the implicit Euler method and in space with the Box method (c.f. [2]), we end up with a nonlinear system of equations. Newton’s method is used to solve these systems, where the required Jacobians are obtained by automatic differentiation (AD) (c.f. [3]). In contrast to approximate Jacobians via finite differences, AD gives exact Jacobians through a source code ...