Generalized GCD for toric Fano varieties

  title={Generalized GCD for toric Fano varieties},
  author={Nathan Mark Grieve},
  journal={Acta Arithmetica},
  • N. Grieve
  • Published 30 April 2019
  • Mathematics
  • Acta Arithmetica
We study the greatest common divisor problem for torus invariant blowing-up morphisms of nonsingular toric Fano varieties. Our main result applies the theory of Okounkov bodies together with an arithmetic form of Cartan's Second Main theorem, which has been established by Ru and Vojta. It also builds on Silverman's geometric concept of greatest common divisor. As a special case of our results, we deduce a bound for the generalized greatest common divisor of pairs of nonzero algebraic numbers. 
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