On the finiteness of maps into simple abelian varieties satisfying certain tangency conditions

Abstract We show that given a simple abelian variety and a normal variety defined over a finitely generated field of characteristic zero, the set of non‐constant morphisms satisfying certain tangency conditions imposed by a Campana orbifold divisor on is finite. To do so, we study the geometry of the scheme parameterizing such morphisms from a smooth curve and show that it admits a quasi‐finite non‐dominant morphism to .