When are multidegrees positive?

The multidegree of a multiprojective variety encodes intersection number of the variety with different products of linear spaces. Characterizing all possible multidegrees of irreducible varieties is a hard problem (with an almost full classification only in the single and bi-graded case). Here we focus only on the support of the multidegrees which turns out to be a special type of polytope. We'll see some applications to Schubert polynomials and mixed volumes of polytopes. This is joint work with Yairon Cid-Ruiz, Bingling Li, Jonathan Montaño, and Naizhen Zhang.