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Effective computations for weakly optimal subvarieties

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arxiv 2105.12760 v1 pith:EP27XGM7 submitted 2021-05-26 math.AG math.NT

Gal Binyamini , Christopher Daw This is my paper · ORCID
classification math.AGmath.NT
keywords weaklyoptimalsubvarietieseffectivefamilieslocusalgebraicarise
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abstract

Ren and the second author established that the weakly optimal subvarieties (e.g. maximal weakly special subvarieties) of a subvariety $V$ of a Shimura variety arise in finitely many families. In this article, we refine this theorem by (1) constructing a finite collection of algebraic families whose fibers are precisely the weakly optimal subvarieties of $V$; (2) obtaining effective degree bounds on the weakly optimal locus and its individual members; (3) describing an effective procedure to determine the weakly optimal locus.

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  1. Hodge theory and o-minimality at CIRM

    math.AG 2025-02 unverdicted

    Survey lecture notes connecting o-minimality, Ax-Schanuel theorems, and the Zilber-Pink conjecture for Hodge loci, with no new results.

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