2009/07/29 by Pietro Corvaja, Corvaja, Pietro, Junjirō Noguchi +1
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.0907.5066
openalex publication_date 2009/07/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 1988 P. Erdös asked if the prime divisors of xn -1 for all n=1,2, >... determine the given integer x; the problem was affirmatively answered by Corrales-Rodorigáñez and R. Schoof in 1997 together with its elliptic version. Analogously, K. Yamanoi proved in 2004 that the support of the pull-backed divisor f*D of an ample divisor on an abelian variety A by an algebraically non-degenerate entire holomorphic curve f: \C → A essentially determines the pair (A, D). By making use of a recent theorem of Noguchi-Winkelmann-Yamanoi in Nevanlinna theory, we here deal with this problem for semi-abelian varieties: namely, given two polarized semi-abelian varieties (A1, D1), (A2,D2) and entire non-degenerate holomorphic curves fi:\C→ Ai, i=1,2, we classify the cases when the inclusion \supp f1^*D1⊂ \supp f2^* D2 holds. We also apply a result of Corvaja-Zannier on linear recurrence sequences to prove an arithmetic counterpart.