2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/149768These are notes of a talk to the International Conference on Algebra in honor of A. I. Mal'tsev, Novosibirsk, USSR, 1989 (to appear in Contemporary Mathematics). The concept of a divisor with complex coefficients on an algebraic curve is introduced. We consider families of complex divisors, or, equivalently, families of invertible sheaves and define Arakelov-type metrics on some invertible sheaves produced from them on the base. We apply this technique to obtain a formula for the measure on the moduli space that gives tachyon correlators in string theory.8 pages, LaTeXAlgebraic GeometryHigh Energy Physics - Theorytext