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arXiv · 1905.00827

Some Remarks on Atypical Intersections

Vahagn Aslanyan
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Abstract

In this paper we show how some known weak forms of the Zilber--Pink conjecture can be strengthened by combining them with the Mordell--Lang conjecture or its variants. We illustrate this idea by proving some theorems on atypical intersections in the semiabelian and modular settings. Given a "finitely generated" set $\Gamma$ with a certain structure, we consider $\Gamma$-special subvarieties -- weakly special subvarieties containing a point of $\Gamma$ -- and show that every variety $V$ contains only finitely many maximal $\Gamma$-atypical subvarieties, i.e. atypical intersections of $V$ with $\Gamma$-special varieties the weakly special closures of which are $\Gamma$-special.

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Vahagn Aslanyan. 2019-05-02. Some Remarks on Atypical Intersections. https://doi.org/10.1090/proc/15611

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