JournalsrlmVol. 25, No. 1pp. 1–36

On torsion anomalous intersections

  • Sara Checcoli

    Université Grenoble I, Saint-Martin-d'Hères, France
  • Francesco Veneziano

    Georg-August-Universität Göttingen, Germany
  • Evelina Viada

    Georg-August-Universität Göttingen, Germany
On torsion anomalous intersections cover
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Abstract

A deep conjecture on torsion anomalous varieties states that if VV is a weak-transverse variety in an abelian variety, then the complement VtaV^{ta} of all VV-torsion anomalous varieties is open and dense in VV. We prove some cases of this conjecture. We show that the VV-torsion anomalous varieties of relative codimension one are non-dense in any weak-transverse variety VV embedded in a product of elliptic curves with CM. We give explicit uniform bounds in the dependence on VV. As an immediate consequence we prove the conjecture for VV of codimension two in a product of CM elliptic curves. We also point out some implications on the effective Mordell-Lang Conjecture.

Cite this article

Sara Checcoli, Francesco Veneziano, Evelina Viada, On torsion anomalous intersections. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 25 (2014), no. 1, pp. 1–36

DOI 10.4171/RLM/666