  These 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.
