A weak version of the Strong Exponential Closure

TL;DR

Under the assumption of Schanuel's Conjecture, the paper proves the existence of generic points in certain algebraic varieties, providing new instances of the Strong Exponential Closure conjecture.

Contribution

It establishes a weak version of the Strong Exponential Closure by assuming Schanuel's Conjecture, demonstrating the existence of generic points in varieties.

Findings

Existence of generic points in varieties over algebraic closure of rationals

Many new instances of Strong Exponential Closure

Conditional proof assuming Schanuel's Conjecture

Abstract

Assuming Schanuel's Conjecture we prove that for any variety V over the algebraic closure over the rational numbers, of dimension n and with dominant projections, there exists a generic point in V. We obtain in this way many instances of the Strong Exponential Closure introduced by Zilber.