Uniqueness theorems for parametrized algebraic curves

Abstract

Abstract. Let L\,... ,Ln be lines in P2 and let f,g:¥l -+ P2 be nonconstant algebraic maps. For certain configurations of lines L\, ..., L" , the hypothesis that, for ; = 1, ... , n , the inverse images f~l(L¡) and g~l(L¡) are equal, not necessarily with the same multiplicities, implies that / is identically equal to g.