Zarhin has extensively studied restrictions placed on the endomorphism algebras of Jacobians J for which the Galois group associated to their 2-torsion is insoluble and "large" (relative to the dimension of J). In this paper we examine what happens when this Galois group merely contains an element of "large" prime order. [ABSTRACT FROM AUTHOR]
In this paper, we first give a slight improvement of Yamanoi's truncated second main theorem for holomorphic maps into abelian varieties. We then use the result to study the uniqueness problem for such maps. The results obtained generalize and improve E. M. Schmid's uniqueness theorem for holomorphic maps into elliptic curves. In the last section, we consider algebraic dependence for a finite collection of holomorphic curves into an abelian variety. [ABSTRACT FROM AUTHOR]
In this paper we prove the following result: Let $X$ be a complex torus and $M$ a normally generated line bundle on $X$; then, for every $p \geq 0$, the line bundle $M^{p+1}$ satisfies Property $ N_{p}$ of Green-Lazarsfeld. [ABSTRACT FROM AUTHOR]