Effective atypical intersections and applications to orbit closures

Gregorio Baldi; David Urbanik

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arXiv · 2406.16628

Effective atypical intersections and applications to orbit closures

Gregorio Baldi·David Urbanik

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Abstract

We propose a unifying setting for dealing with monodromically atypical intersections that goes beyond the usual Zilber-Pink conjecture. In particular we obtain a new proof of finiteness of the maximal atypical orbit closures in each stratum of translation surfaces $\Omega \mathcal{M}_g (\kappa)$, as given by Eskin, Filip, and Wright. We also describe a concrete algorithm, implementable in principle on a computer, which provably computes all maximal orbit closures which are 'atypical' in a sense described by Filip. The same methods also give a general algorithm for computing atypical special loci associated to systems of differential equations, and in particular give an effective and o-minimal free proof of the geometric Zilber-Pink conjecture for variations of mixed Hodge structures.

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BibTeX RIS

Gregorio Baldi, David Urbanik. 2024-06-24. Effective atypical intersections and applications to orbit closures. https://arxiv.org/abs/2406.16628

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