Algebraic and o-minimal flows on complex and real tori

2017/01/31 by Peterzil, Ya'acov, Starchenko, Sergei
#Algebraic Geometry (math.AG) #FOS: Mathematics #Logic (math.LO) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1701.09080

Abstract

We consider the covering map π:ℂⁿ→ \mathbbT of a compact complex torus. Given an algebraic variety X⊆ ℂⁿ we describe the topological closure of π(X) in \mathbb T. We obtain a similar description when \mathbbT is a real torus and X⊆ ℝⁿ is a set definable in an o-minimal structure over the reals.

Related

• Algebraic and o-minimal flows beyond the cocompact case
• o-minimal flows on abelian varieties
• Algebraic flows on commutative complex Lie groups
• O-minimal flows on nilmanifolds
• Coverings over Tori and Topological Approach to Klein's Resolvent Problem