Effective computations for weakly optimal subvarieties

  • Gal Binyamini

    Weizmann Institute of Science, Rehovot, Israel
  • Christopher Daw

    University of Reading, UK
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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 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 fibres are precisely the weakly optimal subvarieties of ; (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.

Cite this article

Gal Binyamini, Christopher Daw, Effective computations for weakly optimal subvarieties. J. Eur. Math. Soc. (2024), published online first

DOI 10.4171/JEMS/1408