Anomalous Subvarieties—Structure Theorems and Applications

  title={Anomalous Subvarieties—Structure Theorems and Applications},
  author={Enrico Bombieri and David Masser and Umberto Zannier},
  journal={International Mathematics Research Notices},
When a fixed algebraic variety in a multiplicative group variety is intersected with the union of all algebraic subgroups of fixed dimension, a key role is played by what we call the anomalous subvarieties. These arise when the algebraic variety meets translates of subgroups in sets larger than expected. We prove a Structure Theorem for the anomalous subvarieties, and we give some applications, emphasizing in particular the case of codimension two. We also state some related conjectures about… 

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