  Let X be a nonsingular projective algebraic variety, and let S be a line
bundle on X. Let A = (a_1,..., a_n) be a vector of integers. Consider a map f
from a pointed curve (C,x_1,...,x_n) to X satisfying the following condition:
the line bundle f*(S) has a meromorphic section with zeroes and poles exactly
at the marked points x_i with orders prescribed by the integers a_i. A
compactification of the space of maps based upon the above condition is given
by the moduli space of stable maps to rubber over X. The main result of the
paper is an explicit formula (in tautological classes) for the push-forward of
the virtual fundamental class of the moduli space of stable maps to rubber over
X via the forgetful morphism to the moduli space of stable maps to X. In case X
is a point, the result here specializes to Pixton's formula for the double
ramification cycle. Applications of the new formula, viewed as calculating
double ramification cycles with target X, are given.
