Generalized GCD for toric Fano varieties
Volume 195 / 2020
Acta Arithmetica 195 (2020), 415-428
MSC: Primary 14G05; Secondary 14C20, 14J45.
DOI: 10.4064/aa190430-5-12
Published online: 8 June 2020
Abstract
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.
