Solving Systems of Equations of Raising-to-Powers Type

2021/03/29 by Gallinaro, Francesco · 1 citation
#03C60 #11F03 #14K12 #Algebraic Geometry (math.AG) #FOS: Mathematics #Logic (math.LO) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2103.15675

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.

Cited by

• Likely intersections in powers of the multiplicative group

Related

• Solutions of equations involving the modular j function
• The theory of exponential sums
• Fulton-Hansen and Barth-Lefschetz Theorems for Subvarieties of Abelian Varieties
• On the exponential algebraic geometry
• Non-archimedean entire curves in closed subvarieties of semi-abelian varieties