Completely decomposable abelian groups any pure subgroup of which is completely decomposable

Computable Completely Decomposable Groups

A completely decomposable group is an abelian group of the form ⊕ i Hi, where Hi ≤ (Q,+). We show that every computable completely decomposable group is ∆5-categorical. We construct a computable completely decomposable group which is not ∆4-categorical, and give an example of a computable completely decomposable group G which is ∆4-categorical but not ∆3-categorical. We also prove that the inde...

Completely Decomposable Jacobian Varieties in New Genera

We present a new technique to study Jacobian variety decompositions using subgroups of the automorphism group of the curve and the corresponding intermediate covers. In particular, this new method allows us to produce many new examples of genera for which there is a curve with completely decomposable Jacobian. These examples greatly extend the list given by Ekedahl and Serre of genera containin...

On the variety parametrizing completely decomposable polynomials

The purpose of this paper is to relate the variety parameterizing completely decomposable homogeneous polynomials of degree d in n+1 variables on an algebraically closed field, called Splitd(P ), with the Grassmannian of n−1 dimensional projective subspaces of P. We compute the dimension of some secant varieties to Splitd(P ) and find a counterexample to a conjecture that wanted its dimension r...

Varieties of Completely Decomposable Forms and Their Secants

This paper is devoted to the study of higher secant varieties of varieties of completely decomposable forms. The main goal is to develop methods to inductively verify the non-defectivity of such secant varieties. As an application of these methods, we will establish the existence of large families of non-defective secant varieties of “small” varieties of completely decomposable forms.

Homotopy theory of simplicial sheaves in completely decomposable topologies