Solving Systems of Equations of RaisingtoPowers Type
Abstract
We address special cases of the analogues of the exponential algebraic closedness conjecture relative to the exponential maps of semiabelian varieties and to the modular $j$ function. In particular, we show that the graph of the exponential of an abelian variety intersects products of free rotund varieties in which the subvariety of the domain is a sufficiently generic linear subspace, and that the graph of $j$ intersects products of free broad varieties in which the subvariety of the domain is a Möbius subvariety.
 Publication:

arXiv eprints
 Pub Date:
 March 2021
 arXiv:
 arXiv:2103.15675
 Bibcode:
 2021arXiv210315675G
 Keywords:

 Mathematics  Logic;
 Mathematics  Algebraic Geometry;
 Mathematics  Number Theory;
 03C60;
 11F03;
 14K12
 EPrint:
 29 pages