Gushel--Mukai varieties: intermediate Jacobians

Mixed Intermediate Jacobians

Existence of good divisors on Mukai varieties

A normal projective variety X is called Fano if a multiple of the anticanonical Weil divisor, −KX , is an ample Cartier divisor. The importance of Fano varieties is twofold, from one side they give, has predicted by Fano [Fa], examples of non rational varieties having plurigenera and irregularity all zero (cfr [Is]); on the other hand they should be the building block of uniruled variety. Indee...

The Intermediate Jacobians of the Theta Divisors of Four-dimensional Principally Polarized Abelian Varieties

Let A be a principally polarized abelian variety of dimension four and let Θ ⊂ A be a symmetric theta-divisor, which we assume to be smooth. Using the Hodge structure on H(Θ) we associate to A two abelian subvarieties J(K) ⊂ J(H) of the intermediate jacobian J(Θ) of Θ of dimensions five and nine respectively. We show that J(H) is generated by the image under the Abel-Jacobi map of the family F ...

Selmer varieties for curves with CM Jacobians

We study the Selmer variety associated to a canonical quotient of the Qp-pro-unipotent fundamental group of a smooth projective curve of genus at least two defined over Q whose Jacobian decomposes into a product of abelian varieties with complex multiplication. Elementary multivariable Iwasawa theory is used to prove dimension bounds, which, in turn, lead to a new proof of Diophantine finitenes...

Delta robot: inverse, direct, and intermediate Jacobians

In the context of a parallel manipulator, inverse and direct Jacobian matrices are known to contain information which helps us identify some of the singular configurations. In this article, we employ kinematic analysis for the Delta robot to derive the velocity of the end-effector in terms of the angular joint velocities, thus yielding the Jacobian matrices. Setting their determinants to zero, ...