The concept of multidegrees provides the right generalization of the degree of a projective variety to a multiprojective setting. The study of multidegrees goes back to seminal work by van der Waerden in 1929. We will present a complete characterization of the positivity of multidegrees. This characterization will show that the positive multidegrees of a multiprojective variety form a discrete polymatroid, which is a very special type of lattice polytope. Finally, we will apply our methods on multidegrees to settle a conjecture of Monical, Tokcan, and Yong for (double) Schubert polynomials.
