Universal generators for varieties of nuclear spaces

Model Theory of universal covering spaces of complex algebraic varieties

We ask whether the notion of a homotopy class of a path on a complex algebraic variety admits a purely algebraic characterisation, and reformulate this question as a question of categoricity of the universal covering space of a complex algebraic variety in a natural countable in nitary language. We provide partial positive results towards the question. Assuming a conjecture of Shafarevich and s...

Generators of lattice varieties

Although it is well known that the variety of all lattices is generated by the subclass of finite lattices, there are lattice varieties which are not generated by their finite members . In fact, there are modular varieties which are not even generated by their finite dimensional members [3]. At the present t ime it is not known if the variety of all modular lattices is generated by its finite o...

Varieties of coarse spaces

A class M of coarse spaces is called a variety if M is closed under formation of subspaces, coarse images and products. We classify the varieties of coarse spaces and, in particular, show that if a variety M contains an unbounded metric space then M is the variety of all coarse spaces.

Bounded generators of linear spaces

Centrally symmetric generators in toric Fano varieties

We give a structure theorem for n-dimensional smooth toric Fano varieties whose associated polytope has “many” pairs of centrally symmetric vertices. Introduction. Smooth toric Fano varieties, together with their equivariant birational contractions, have been intensively studied in recent years: see [WW82, Bat82, Bat99, Sat00, Bon00, Cas01b, Cas01c, Sat02]. In some cases, the toric case has bee...