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<p>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 <i>j</i> function. In particular, we show that the graph of the exponential of an abelian variety intersects products of rotund varieties in which the subvariety of the domain is a sufficiently generic linear subspace, and that the graph of <i>j</i> intersects products of free broad varieties in which the subvariety of the domain is a Möbius subvariety.</p>

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Solving systems of equations of raising-to-powers type

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年7月30日

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  • Francesco Paolo Gallinaro

摘要

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 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.